I was doing lateral shoulder raises last night, and it feels as if my left lat is getting much tighter and shows sitting higher in the mirror than my right. I'm right handed, is there any common cause of this?
I am assuming you mean your left "deltoid?"
There are a variety of reasons ranging from musculoskeletal gashitis to a bad swolfie angle.
Chances are it is a joyous combination of tight pecs, poor thoracic spine mobility, poor joint capsule mobility, too much one-handed reading, tight lats (the real ones), poorly controlled rotator cuff, poor back training/strength/activation, crud core strength and the fact you possibly owned a Ben Sherman shirt at some point in your life.
In other words: there are few symptoms of deeper problems that can cause sub-luxation (super- is less likely) in your glenohumeral joint, as well as a few simple mobility drills to get familiar with to determine which is which.
Hit up MobilityWOD and YouTube "shoulder mobility."