He had younger siblings looking up on him.

Is this sentence above grammatically correct?

Yes, the sentence is grammatically correct.

He had younger siblings looking up to him.

Is this sentence above grammatically correct?

Yes, the sentence "He had younger siblings looking up to him" is also grammatically correct.

Which one is correct in a sense that their father just died and his siblings look up to him to take care of them.

The correct sentence for that scenario would be:

"He had younger siblings looking up to him to take care of them."