How to control throttle without changing receiver
 

Can you map the left forward and back stick on a programmable transmitter to a servo output to control athrottle ring orlever, or do you have to put in a different type of receiver.imtalking about when the receiver has a built-in esc

I've seen, and used, several different types of programmable transmitters and the first 4 channels in all of them were fixed. I would think, however, than an OpenTX transmitter might be programmed to put the throttle stick on any channel but that would be at the processor level, not at the user level. But the more important question is what channel your receiver's built-in ESC is on? With that answer you might also be able to use a mix to map your throttle to the ESC.

Yes, an OpenTX system can use any stick, switch, slider, knob to control any channel. But the receiver in question must have unused channels (as the normal throttle will not be used) AND one must make sure the receiver is compatible either with the native protocols the transmitter comes with, or that the transmitter can be made compatible with an add-on multi-protocol module. The first part is pretty easy for anyone. The second means a deeper dive into what the receiver requires. Between expense and time it takes to come up to speed on both OpenTX (and the module, if purchased) and learning the details around protocols, so you can judge what to buy....it is far, far easier to just get a new receiver that is known to work with your current radio.