In reply, Lancashire lost two early wickets with Luis Reece (5) and Rob Jones (2) falling cheaply but Clark joined opening batsman Smith at the crease and the pair played nicely for the third wicket.
Smith (34) and Clark (48) put on 78 before the latter was dismissed by bowler Tom Taylor. Bailey and Stephen Parry lost their wickets cheaply before Smith was caught behind off the bowling Greg Cork, son of former Lancashire bowler Dominic.
Bradley Yates (16) and Arron Lilley (23) contributed with late runs as Lancashire were bowled out for 150, a first innings lead of 46.
Derbyshire's second innings saw much better batting from the visitors and they closed the day 123/3, a lead of 77 going into the final day.