So I've had several Diawa spinning reels over the years. My current reel (a Lexa) has always had a drag that "sticks." 

It has been like this since I bought it. Basically, when I pull the line it does not want to leave the spool, even set at low drag. Same for hook sets.

Anyone ideas on a fix?

I would remove the spool from the reel, take apart the drag stack and check for debris or a damaged drag washer.  I would also check the roller bearing but I think it would be unlikely that it is causing this issue. 

Maybe clean drag stack and add some grease would help. Alternatively upgrade to smooth carbon drag if you have felt drag.

All my Daiwas, have similar issue, not stick but kind of tighter than usual when store with drag set. Every time I wanna use the reel, I loosened the drag pull line out a few feet and set the drag where I want. 

 If it never worked right, there might be something wrong with it.  I'd take it apart and see if something is misaligned, missing or broken.  

Go to “Smooth Drags” they make replacement drugs for all reels.

Tom