A Lamport clock is two rules: tick your counter on every event, and on receiving a message raise your counter to at least the sender's stamp before ticking.

That guarantees a → b implies L(a) < L(b). It is all the clock ever claimed, and the converse is false:

| pair | lamport | causality | | --- | --- | --- | | a2, b2 | 2 < 3 | happens-before | | c1, a2 | 1 < 2 | concurrent | | b1, c1 | 1 = 1 | concurrent |

c1 has a smaller stamp than a2 and there is no causal path between them. So "last write wins by Lamport timestamp" is picking an arbitrary winner among concurrent writes and presenting it as an answer.