In the NEMA spec the L6-20P means "L" for locking, "-20" means 20 amps, "P" means plug", and "6" means the arbitrary distinction of a type 6 connection.
What those connection descriptions mean can be found on a number of websites and reference books, Wikipedia is as good of a source as any on this. https://en.wikipedia.org/wiki/NEMA_connector
The type 6 outlet would have a ground and two hot contacts. Putting a L6-20R receptacle for your device with a L6-20P plug is relatively trivial. Replace the breaker in the breaker box with a 20 amp breaker. Then replace the outlet. The neutral wire should be capped off and tucked away in the electrical box so it doesn't touch anything and so if you need that neutral wire later it is there. The old oven plug likely has #6 or #8 wire which may be quite large for the outlet you are putting in its place. A short "pigtail" of #10 or #12 wire can fix that.
Another option, and one that should be taken with care, is to leave the oven outlet and find an adapter. I say care should be taken as if there is an overload the original 40 or 50 amps breaker will not trip as quickly as with a 20 amp breaker. The breaker exists primarily to protect the wires in the walls, not the device or the user.
There are extension cords for both the 14-50 outlet you have and the L6-20 outlet you want. The 14-50 is common for RVs, EVs, and portable generators and so extension cords will be carried by many hardware stores. Maybe not in stock but they can order it for you. The L6-20 is common as well, I believe for welders, and so again most any hardware store will carry it and be available in stock or ordered for delivery quickly.
I'd consider this of little more difficulty than replacing a common household outlet. If this looks like too much for you then call a professional.
My disclaimer: I am not a professional electrician. I studied electrical engineering at university but that's quite different than being an electrician. An electrician will know what is code, I know only that my house didn't burn down from my DIY wiring... yet.