While transactions are signed, the signature does not currently cover all the data in a transaction that is hashed to create the transaction hash. Thus, while uncommon, it is possible for a node on the network to change a transaction you send in such a way that the hash is invalidated. Note that this just changes the hash; the output of the transaction remains the same and the bitcoins will go to their intended recipient.
Before SegWit, tx ids were malleable and thus a lightning node could lose track of its channel open tx (and any txs that depend on it) while it's getting confirmed.
Lightning didn't need larger blocks but the transaction malleability fix that SegWit included:
Before SegWit, tx ids were malleable and thus a lightning node could lose track of its channel open tx (and any txs that depend on it) while it's getting confirmed.