Bolton stay rock bottom, with their losing streak in the league extending to six games.
Their defending was generally poor, with Bogdan - in the team for the injured Jussi Jaaskelainen - enduring a particularly bad afternoon, letting Sturridge's shot from the edge of the box loop in off him in the 25th minute when he should have saved, and then two minutes later parrying David Luiz's strike straight at the feet of Lampard, who tucked it away gleefully.
Bolton manager Owen Coyle expressed his sympathy for the Hungarian stopper.
"Young Adam Bogdan is going to have a terrific career, there is no doubt about it," Coyle said.
"But the third and fourth goals should have been basic saves and that is the thing with a goalkeeper - there is no hiding place if they make a mistake, it results in a goal.
"I feel for the kid, but he has to show the character to come through that."