People almost always want to be able to turn lights in an out building on and off from the house. In other words you don't want to walk back out because you forgot to turn the lights off. Suggest you pull a 12/3 cable for a 3-way switch in the house for the shop lights.

Grease, I said to use (3) #2 and (1) #6, never mentioned #4, as you have in your materials list.

Medic, yes any feeder now needs an equipment ground, no matter in a detached structure or not.

The 3 wire feeder is no longer allowed.

On another note,

This is as good a place as any to mention this, Table 310.15 (B) 6 of the NEC is not allowed for subpanel feeders. I had misused this table myself in the past. So, #4 copper, for example, cannot be used to feed a 100 amp subpanel, only to feed the main service.

All experts, and any others that offer advice here, please take notice, and cease and desist from offering Table 310.15 (B) 6 wire sizes for residential feeders.