I would like to know what size wire I need to go 150 ft. It will feed a subpanel in my out building which will have a air compressor 220v 30amp. And 110 lighting.

Before we get started I'd like to narrow this down, do you really mean 220 and not 240? Where are you located?

The motor tag reads 220V. Location is Tampa Florida.

And what voltage do you get when you put your test leads across your hots? I asked about location because its important for us to know what country you are in, voltage varies. I will wait for TK or Stanforty to advise on the exact gauge wire. I rarely run this length wire for 240 since I am not a licensed electrician.

Missing some detail, such as horsepower of motor, and wattage or amps of lighting.

Assuming a total of 50 amp 240 volt load at 150 feet, #6 copper wire or #4 aluminum will be sufficient.