D&D 5E Warlock's Fiendish Vigor and spell slots

[Undrhil]

I know the invocation says that you can cast it "at will" and this would be at the lowest level available for the spell, which is first level. But, once I have this invocation, can I cast False Life using a spell slot, therefore at a higher level than first?

 

[Leatherhead]

The invocation neither lets you "learn" the spell, nor does it let you cast the spell with spell slots.

There are other Warlock abilities and invocations that are explicitly worded to let you do such things, however this is not one of them.