This seems to be a direct translation from English. In Irish, if you "let go", you use the verb scaoil, or bog. lig is never used natively in this sense.
You can see it here, if you ctrl-f "to let go". You can also see it under scaoil's entry
This sentence would more mean: I allow him to go.
Yeah. I took the sentence as quoting Frozen.
When presented with the sentence, I thought they were intending it to mean "I let (= allow) him go" which, I think, should be "ligim dó dul".
You're right traditionally. Although native speakers might not express it with the traditionally correct "do"
The Frozen line would be Scaoilim é...
I would say scaoilim leis.
Odd way of saying it. :-(