Skydive Pilot reported a conflict during the takeoff lift with a light twin aircraft landing on the opposite direction runway. A rejected takeoff was necessary to avoid a collision.

Narrative

Routine takeoff on [Runway] XX (6th one today); made usual call 'ZZZ traffic; Callsign X; departing XX.'. (This was later verified by another person on the ground monitoring Advisory.) Turned onto runway; started takeoff roll; lifted off; saw landing lights on a light twin on final approach on [Runway] XY. They had made no calls at all on Advisory. (Also confirmed by the listener on the ground.) Hoped for a second that the twin was just making a low approach and saw us; but they continued approach. I pulled power; pitched down; called 'ZZZ; aborting takeoff.' Was able to set the plane down and exit the runway as the twin continued the approach. About that time; the twin pilot called 'Going around' and tried to claim that he had made appropriate calls and that I had not. I suspect that the twin pilot did not turn on his landing lights until I had already taken off. Approaching against the rest of the traffic today; with the low light under the overcast; a white airplane would not be very visible without those lights.