Jerry,
I have the same setup.
You just need a PTT cable from 991A to LA-1K.? I am using 8 pins DIN plug and RCA plug in the other end.
It will be pin 2 TX GND and pin 3 GND.? More in for can be found on page 19 of the 991A manual under TUN/LIN drawing.
Or you could simply use a foot switch.
73, Komkit W3KIT