First, make sure the codes are all erased from the buttons by holding the #1 and #3 button for a while till the light blinks rapidly.
Then, take a working transmitter, put it next to the HomeLink, and simultaneously hold the button you want to program and the transmitter that came with the garage door. After that's trained, or the light changes speed of blinking, go to the garage door opener itself, find the train button, press it. Run back to the car, that needs to be parked nearby, or in the garage... Press and hold the button you previously trained for about a minute. Then, leave it all be for a few minutes then it should all work. Good luck!
The owners manual has a decent explanation too - but I guess you may not have one handy! :)
P.S. - Not sure about the '97 LHS but my Sebring just had it all built into the sun visor. If yours is connected to the information display, it works the same, just the display tells you when each training step is complete.