Only the UTXO set is required to determine whether the inputs for a transaction are available for spending or the funding output for a channel remains unspent. Just like any other full nodes, pruned nodes have processed the entire blockchain and derived the current chainstate by applying all transactions to arrive at the same UTXO set.
I do not consider myself an expert regarding Core Lightning, but the README on the Core Lightning GitHub project states that a pruned node is sufficient to run Core Lightning without further qualifications, so I would read that as Core Lightning having its full capabilities when paired with a pruned node.
LND used to require a full node with txindex. Since pruning is incompatible with the txindex option, this meant that LND could not be used with pruned full nodes. Since LND 0.13 (released in June 2021), LND can also be run with a pruned node, although the documentation states that pairing LND with a node that uses the txindex option will be more performant.
