Two devices change the same thing while apart. When they meet, something has to choose. LWW chooses the later write.
For interface state (which tabs are open, how the panes are arranged) this is the right amount of machinery. Nobody wants a merge dialogue about a divider position, and losing one of two conflicting layouts costs a drag to fix.
Where it goes wrong
Wall-clock time. Machine clocks differ by seconds, sometimes minutes. Deciding "later" by comparing two timestamps taken on two machines means the device with the faster clock wins arguments it should lose, permanently and invisibly.
The fix is a monotonic sequence assigned by whatever both parties agree on: a server sequence number, or a logical clock. "Later" then means after in a causal sense, which is the thing you actually meant.
Granularity. LWW over a whole object throws away non-conflicting changes: if one device moved a divider and the other opened a tab, resolving at the object level loses one of them although they do not conflict at all. Resolving per field keeps both.
Empty wins. The most damaging version is a device that syncs an empty state during startup, before it has loaded anything, and wins on recency, wiping every other device. A rule of "later wins" needs a companion rule that an empty state is never authoritative.
What LWW is not for
Documents and text. Losing half a paragraph because two people typed at once is not an acceptable outcome, and that is what CRDTs and operational transforms exist for. LWW is for state where a lost update costs a gesture, not work.