if the lights or air conditioner were forgotten to be switched for Shabbos on can the goy be asked indirectly to switch them on
A non-Jew cannot be asked to turn on the lights even indirectly, because a Jew cannot have any direct benefit from a melacha preformed by a non-Jew for a Jew.
Regarding turning on the AC- if it is extremely uncomfortable it is permitted.
All the best
Turning on AC- Minchas Yitzchak 3:23, Shemiras Shabbos Kehilchaso 13:39 and 30:11 (cf. Igros Moshe Y”D 3 47:2)