While it is best to be on its own circuit it is possible to run a 10,000 Btu
AC on a circuit that is only using a couple of lights. If there are other
appliances, then no.

I agree. A 10,000 BTU a/c uses approx 10 amps. If you have a 20 amp
circuit with light load, you could get away with it. If it was a 15
amp circuit, I'm not sure it would hold when the compressor initially
starts up.

It's very possible a dedicated outlet already exists. Have someone
turn off each breaker and see if anything else is on that outlet.