I have been using Lucky's on my laptop for a while now, no issues, my native screen res is 1440x900, i do NOT change the laptop resolution at all.
Put game on 1024x768 windowed only (not fullscreen windowed) then move to top left corner of screen).
Using the new 5.3, i was able to complete all missions (fully geared 50) except for Clouds, only reason clouds didnt work was cause the generators required my proton torpedos. After i unequipped them, it ran perfectly, ran every daily today with 100% success (except for 2 that arent in yet of course). When doing dailies, make sure you send out at least one companion to do crew skills otherwise it sometimes doesnt accept the 2nd mission complete when done with a daily quest.
This is an older laptop (duo core cpu 2.2, 9800GTS 1Gig, win 7, 8 gigs ram)
If you are running into issues with lower level ones, make SURE you put each upgrade in or it will NOT WORK.(or very low success rate) Ezran for example is only req. level 28 on character but absolutely has to have the shield generator level 3 which requires character level 29 (basically hit 27, do your dailies and pvp, then some of your class story line to hit 29, then back to botting)