Lag is used after these nouns:
time

badly, seriously, well
behind
She did well in her first year but then started to lag behind.

behind
Catering salaries lag far behind those of other sectors.
Britain still lags badly behind the rest of Europe on this.

lag far behind (sb/sth), lag way behind (sb/sth), lag well behind (sb/sth)
The party is still lagging way behind in the opinion polls.

Lag is used with these nouns as the object:
pipe