You'll never be able to do that with just a wire in that controller, or any controller really.
Depending on how timing specific this is there are a couple of options.
The easiest way to do what you are wanting would be to install some small switch under the LT assembly so that it gets pressed only when the LT is pulled all the way. Then wire that switch up to be a duplicate of the LSC button. You pull the Trigger, the Trigger action happens and then it presses the switch and the switch presses LSC.
Now, if you are trying to duplicate some button sequence that requires a specific timing to pull it off, like after you press LT you must wait some fraction of a second and then press LSC (which is called a macro) then you'll need some kind of micro controller and code written up to handle doing that correctly.