Lightning bolt is on my staff, but where is the skill shown to add a gem to it?

I get a level 2 lightning bolt and +2 lightening levels from equipping my staff.

But I don't see that skill anywhere in the normal listing of level 1 ... level 3 ... etc to engrave or do anything to it.

Is lightning bolt not a normal spell that one could use even without the staff giving it to me? Or in general, are there some spells like that that are only given my items and not normal skills?

If you engrave a support gem it will show at the top when pressing G