I just got a lamda class shuttle and I need to make a list, The other ships I have are a TIE defender, TIE advanced(not the raider), TIE fighter

What list can I make?

Not a very promising selection I am afraid. The shuttle is usually used to carry Palpatine (who comes in the Raider). The Tie Advanced is poor without the Title (which also comes with the Raider) and the Tie Defender is weak without the Titles that come with Imperial Veterans.

Are you willing to spend any more cash or are you looking to work with just the ship you have listed?

I am willing to spend cash, now I know what to get next

Raider + imp vets +tie/fo and you have a bucketload of top performance options.

In the meantime try vader/ vessary/howlrunner?