来なくて

don’t have to come

→ 来る
来 come; arrive + なくて Negative te-form
verb · informal Uncommon #17,079
don’t have to come 来なくていい means that coming is not necessary.
JA: あしたは、来なくていいよ。
EN: You don’t have to come tomorrow.
Conjugation of 来る

明日は来なくていいですよ。

You don't need to come tomorrow.

来なくてもよかったのに。

You didn't have to come.

もう来なくて結構です

You don't need to come anymore.

— 紅夢 (1991)

彼女がここに来ても来なくても私には関係ない。

It doesn’t matter to me whether she comes here or not.

だからお前来なくていいよ

So you don't need to come.

— 箪笥<たんす> (2003)

来なくていいのに…

You didn't have to come...

— 別れる決心 (2022)

明日は来なくてもいいですよ。

You don’t have to come tomorrow.

あしたは、来なくていいよ。

You don't have to come tomorrow.

彼女が来なくてとてもがっかりした。

I was very disappointed that she didn't come.

先週の月曜からメアリーから連絡が来なくてさ、トムが心配してるんだ。

Tom's worried because he hasn't heard from Mary since last Monday.

ここには来なくてもいいんですよ。

You don't have to come here.

来なくていい

You don't need to come.

— 別れる決心 (2022)

じゃ来なくていい

Then don't bother coming.

— ほんとうのピノッキオ (2019)