Lyth, named in the touring party to West Indies in April and May, moved his overnight 53 on to 113, before being dismissed by Adam Riley (3-90).
Will Rhodes (61) and Andy Hodd (57) helped push Yorkshire to 372 all out.
MCC closed on 13-0 in their second innings, trailing by 138 runs, with England captain Alistair Cook unbeaten on two and Nick Compton on seven.
Cook, who scored only three in the first innings, faced 16 balls as the opening pair saw out the final five overs of the day.
Yorkshire began day two on 82-2 and Lyth and Steven Patterson (36) took their third-wicket partnership to 91, before Patterson became Riley’s first victim.
Jonny Bairstow fell for a sixth-ball duck and Lyth was fifth man out with the score on 195, but a century partnership between Rhodes and Hodd gave Yorkshire a first-innings lead.
Adil Rashid hit five fours in making 42 from 57 balls to push Yorkshire’s total past 350.