I have found running his minions in kill teams is really effective.
Generally, I have a beckoner, depleted and Illuminated run together.
Becky walks, lures the depleted and pushes forward. Illuminated double walks. Depleted double walks and pushes towards becky or illuminated.
If I take two such kill teams, that makes 6 models near mid field by the end of turn 1.
I know people tend to crap all over beckoners but I find them absolutely invaluable in a Lynch crew.
Also, always take burying Huggy. Being able to recklessly launch him at a juicy model or just to jam is silly.
Lynch is probably one of, if not the, best at running entirely in theme.