It seems that
無くて is an inflection
with the following forms:
- Te form: indicates connective form.
Definition of 無くて
- (adj-i) nonexistent; not being (there)
There is not much difference between the two opinions.
- unpossessed; unowned; not had
- indicates negation, inexperience, unnecessariness or impossibility
- (aux-adj) (after the ren'youkei form of an adjective) not ...
- (after the -te form of a verb) to not be...; to have not ...