Looks like it’s by design (at least since 4.x) and happens not only with influxdb but also JDBC (see item.persistence.lastUpdate() not always working ) and others persistence engines (not with mapdb however).
Important: this only happens in the rules which react to changes/updates to the ITEM you do lastUpdate on. In any other rules, lastUpdate works fine.
This will be kinda "fixed/reverted/no guilt admitted in 4.3, see: item.persistence.lastUpdate() not always working
Temporary workaround you can use now:
replace lastUpdate in ITEM chaning DSL rules to ITEM.previousState.getTimestamp