Can I connect a 120V output from a generator to a 240V L14 receptor ?

[alfreds-77]

Greetings. I have generator with only 120 V output. It has both standard 120V outlets and a TT-30. A friend's cabin is wired for alternative generator power with a transfer switch to be used during power failures. There is a L14-30 male receptor on the outside of the cabin which connects to the L14-30 female end of a L14-30 cable. (So, I believe it is designed to take the output from a 120V/240V generator). All the appliances and load that are wired for use on alternative power (i.e. when the transfer switch is thrown to the generator side) are 120V only. (There is a 240V dryer but it is not wired for use, and cannot be used, on alternative power.

My question : is it possible to connect either of the 120V outputs from my generator to the L14-30 male receptor to run my load (which as mentioned, is all 120V) ? If so, how would I go about doing that ? Would I have to wire my own custom cable ? And, if so, I assume I'd connect ground to ground and neutral to neutral. But which of the 2 live wires from the L14-30 would I connect to the live wire from the 120V ? Or would I connect them both ?

Or are their adapter cables available on the market I should consider ?