The ignition will not turn

I would not as it will get gummy and cause more problems. Does it move at all? If not it likely is not something that lubricant will cure but a bad ignition cylinder or damaged key.

The most likely cause would be that the tumblers that release the cylinder when the key is inserted have a problem. The repair would be to remove and replace the key cylinder.
When the key can be moved this is not a difficult job, however if it does not move with the key it get's much more difficult. Graphite lock lube might help but it usually only works on pins that already move.

You can try a couple "tricks" that might work. One is to tap on the key with it inserted to get the tumblers to shift. Another is to hold the steering wheel and jiggle it back/forth while trying to turn the key, sometimes the motion will free up a sticking cylinder. Next would be a new key, the Hyundai keys seem to wear out pretty fast, If yours are worn you can have a dealer or good locksmith cut you a new one using the factory code.

The last option is to change out the cylinder itself. For that you would normally remove the panel under the dash, turn the key to the on position and depress the cylinder release pin to remove it. In this situation where the key does not move a locksmith can sometimes use a pick and get it to move and release. Other times it will need to be drilled out.