Ligation Independent Cloning literally says no need Ligation, but it still needs ligase to anneal the fragment to vector. And the Protocol used T4 DNA Ligase for anneal process. What does this mean "Ligation Independent"?
T4 DNA polymerase has two enzymatic activities: 5'–3' polymerase activity and 3'–5' exonuclease activity. Ligation-independent cloning is based on the generation of complementary single stranded DNA overhangs in vector and insert using the proofreading capability of T4 DNA polymerase. No restriction enzymes or ligase activity is required for cloning.
The long cohesion end needs to anneal to the plasmid vector and it requires T4 DNA Ligase. At this point, it does need Ligase. Why is "Ligation Independent"?
As far as I understand LIC, the long overhangs allow a stable association between the fragments, and the annealed fragments are repaired through the transformation/replication process.