The only remotes Lionel is currently manufacturing are the Universal Remote and CAB1L. The CAB1L requires either a CAB1L Base or BASE 2 and is compatible with the BASE3 when it arrives.
You would need to upgrade to a BASE2, and LCS Wifi module to run Lionel trains with the current iCab app. If you want to use the new soon-to-be-released Lionel CAB3 app, you must purchase a BASE3. The CAB3 app by itself will only run Bluetooth equipped engines, if you only have newer Legacy engines with Bluetooth this could also be an option for you.
Given all of the equipment you have now and assuming you have the MTH cable that connects your TIU to your TMCC Base, you can add an MTH WIU to your TIU and control all of your MTH & Lionel engines using the MTH App (or DCS Remote). The only thing you'll need to purchase is a WIU (around $160) and the Premium App upgrade ($25).