The Carista and the VX Diag (Techstream) are the cheapest way, but any TPMS scanner/programmer that works with Toyotas should also work in this case. Like the Autel listed above.
There is a lot of conflated information here, since most of this thread isn't differentiating between different years of LC and LX, and I don't know if anyone knows how much the features being talked about here overlap.
If you have a single "Reset" button in the knee panel under the steering wheel, that button has nothing to do with programming sensors. Its only purpose is in a functioning TPM system where all sensors are registered and working, and you want to reset the trigger pressure that activates the low-pressure indicator in the combi-meter.
I have a 2010 LX and as far as i know, it has no ability to "learn" new codes. If you wish to change sensors, you must program them through the OBDII port one way or another.
There is talk about other functions being completely wiped by draining capacitors in this thread. I'm not sure if that actually works on a LX (or at least my model year LX), because i'm pretty sure the LX saves many settings to the hard drive in the infotainment system. This would be saved in non-volatile memory that can survive a complete power drain. I have never seen a list discussing how much is saved as it pertains to drivetrain ECUs, or if it's only user settings.