First, let's cover the basics.

#1 power supplies power the load- in this case, the trains, and any cars that have lights or draw power. Again, simply put, the power supply matches the load. Track is just a conduit between the power supply and the load. It doesn't matter if you have 300 feet of track or 12 feet of track, the power supply(transformer) is sized based on load (the trains and any accessories) you want to run. Again, I see this near daily in some train forum that someone added track, do I need a bigger power supply and the answer is no- not unless you also added more trains running off the same power source.

Which leads to #2, Track is a connection at each end. If you only have one power entry point, think of this as taking extension cords and plugging them into each other to make a really long cord. Is any one of those connections is loose or intermittent contact, then as the train is down at the far end- it depends on all those contacts being perfect. Also, depending only on the metal rails for power- each contact, each inch of rail is resistance. This is why power distribution- having power entry back into the rail system heavier copper wire with less resistance than the rails and all those connections to the opposite side of the loop improves the situation.

#3 Becomes the controversial point- yes, I say you can use 2 Lionchief DC wall power packs. When I first got back into trains, this is how I powered my extended over 100 feet of track layout in one room, down the hallway and back. Because it's DC and the fastrack power entry jacks are wired the same, there is low risk of the 2 power supplies being wired to the track incorrectly. Between the resistance of the track, the already known weak connections, injecting a power source that is the same polarity and voltage will boost the power in the places where it previously dropped. However, not, this is not a fix all. The real answer is either bus or star power wiring with multiple power entry points every couple of track sections (I use the rule of 4-6 track pieces then a power entry connection) for my permanent layout.

Your product number is

SKU: 2023130

Being that was from the 2020 catalog series- that is pre-Bluetooth 5.0 so the below statement applies to your hardware. As a side note, because Lionel discontinued the license, they cannot sell that set anymore and have removed almost any and all reference to it except for the product page. Obviously you might find product at dealers- but not direct from Lionel. https://ogrforum.com/...c/159096765338291262

Also, something else to keep in mind. Depending on what model your Lionchief electronics used, many used BLE version 4 (Bluetooth Low Energy). that should make something in your head click- low energy? That sounds like low power- aka not transmitting powerful radio waves. So what it means is, unless that specific train model has the newer Lionchief 5.0 which now no longer has the BLE 4.0 module, you might see radio range dropouts from the remote control. So if you get to the point where you have a large layout that is approaching distance where the operator and the remote could be near 20 feet away from the engine at times- then you might see these dropouts.

Most likely, you have a power dropout issue from your initial post and that is common with any track system relying solely on one power entry point and no distributed power entry with multiple feeders. Relying on mechanical track joints of pins and hollow rail is just not great reliable power transfer.

Also, another talking  point about Lionel trains and expansion of a layout to include more trains and more accessories.

Yes, ideally, at some point, you may need more power and at that point or a point where you add an engine, car, or accessory that demands AC power. Here is the rub, Lionel made recent modern trains like Lionchief and possibly modern Legacy as well as plug and play accessories that will accept DC. However, they also made and even inlcuded cars in DC lionchief sets that actually want and need AC to operate. An example of these are the searchlight cars in the Lionchief Army set. The light will not rotate powered by DC. Even worse, some older equipment- anything that used TRIACs in the control circuit to control AC power can get stuck on with DC power which may damage the engine or accessory.

So your question is not wrong, you do have at some point a split in the road. Yes, technically, with the specific question you asked of can he run those with 2 DC lionchief power packs, the answer is yes. All of that equipment is DC compatible. At some point, as more trains and possibly older trains, cars, and accessories are added, you may run into an item that demands AC power and is damaged by DC power.

Last, I failed to answer this question "Also can he run both trains with a single Lion Chief controller?"

I think the answer is no with Bluetooth enabled Lionchief engines. I could be wrong. I do not have 2 identical engines to test this with. The reason is, the bluetooth is a 2 way communication (at least acknowledgement of connection) with the remote. So when it pairs with one engine, then the other engine cannot pair with the single remote. Older pre-bluetooth Lionchief engines used a different radio system and thus they in theory can be driven from one remote. In fact, I was just able to test this using 2 Albert Hall Lionchief engines I know to be the older Lionchief before Bluetooth and they could be run together from one remote. Again, my guess is that bluetooth enabled engines, due to the way they pair to a remote or pair to the bluetooth app, I'm not sure if with 2 engines one will just read the signal from the remote paired with the other engine. Hopefully someone with a BLE 4.0 engine pair can comment.

"Last, I failed to answer this question "Also can he run both trains with a single Lion Chief controller?"

I think the answer is no with Bluetooth enabled Lionchief engines."

There is an exception, and a bargain one .  If you purchase the LionChief Universal Remote (about $45-50 usually) you can control up to 3 LionChief/Bluetooth equipped locos from the one remote in command mode. This includes recent Legacy locos equipped with Bluetooth and almost every LionChief and LionChief + (and LionChief + 2.0) made over the last decade or so.

As pointed out, the Lionel Universal controller can control three LC bluetooth equipped engines, although not simultaneously. It should however be noted that the basic bluetooth system protocol is not limited to a single communication connection at a time. The bluetooth based BlueRailTrains system can simultaneously connect to a number of locos using the multi-train option in the app. I have done this many times. Also, there are special provisions for consisting in the multi-train mode.

" although not simultaneously. "

Well, if you push a button, you can choose the loco you control at that moment.  Three locos in the Universal Remote at a time.

@Landsteiner posted:

" although not simultaneously. "

Well, if you push a button, you can choose the loco you control at that moment.  Three locos in the Universal Remote at a time.

Yes, three locomotives with one Universal Remote and the Remote's range is at least sufficient for a medium sized layouts. I have been able to control my LionChief locomotives and Bluetooth equipped Legacy locomotives from as far away as 35 feet ( as far as I could go in my basement). 

Three locomotives as a time does not mean that you can only own three LionChief/Bluetooth equipped locomotives. You can have as many as you want with one Universal Remote, it just means you can only run three of them at once. It is however, easy and quick to switch out locomotives with the Universal Remote.

Update, I found a local friend with 2 of the Star Trek Engines SKU: 2023130 and was able to test. At first the remote connected to both engines and stopped the chirping not connected sound, however, neither engine would move. A few tries later of power cycle the engines and the remote, and then both could be driven from the single remote. So it works, and getting it synced up might at first be a hit or miss, but in theory- these 2 engines will work.