Lambert was optioned to Triple-A Charlotte on Friday.
The right-hander earned his first major-league win Tuesday against the Athletics when he allowed a run in five innings, but he'll head back to the minors since Lance Lynn (knee) was reinstated from the 10-day injured list to start Sunday's game against the Red Sox. Lambert has posted a 6.23 ERA and 1.69 WHIP in 13 innings across four appearances (three starts) in the majors this year, and he'll be a candidate to rejoin the White Sox if they need a spot starter.