Darren Kenton had headed the opener for Leicester but Jon Parkin quickly equalised from six yards.
Ricardo Fuller's penalty, after he had been fouled by Kenton, put Stoke ahead only for Elvis Hammond to restore parity with a sidefoot finish.
Sidibe finished off a fine pass from Ricardo Fuller with 12 minutes left to put Stoke 3-2 up and Lawrence rounded off the win with a smart shot.
"He's got to learn to manage his temper, but all the players like him and respect him because he's got so much talent and ability.
"He can win you games on his own. He scored a goal and he's had a hand in the other three and played really well.
"He looked a handful and having missed quite a few games, he owes quite a bit back to the dressing room."
Leicester manager Rob Kelly:
"We still need a few more points (to survive). 50 points is your benchmark when you kick off in August and you want to hit it as early as possible.
"We're still striving to do that but whether even that will be enough this season remains to be seen.
"You've just got to get on and try and win football matches. We're aware that we're not past our first benchmark and we don't want anything creeping up on us."
Stoke: Simonsen, Hoefkens, Zakuani, Fortune, Higginbotham, Lawrence, Eustace, Russell (Dickinson 46), Martin (Hendrie 73), Parkin (Sidibe 63), Fuller.
Subs Not Used: Hoult, Vass. Booked: Fuller.
Goals: Parkin 18, Fuller 29 pen, Sidibe 79, Lawrence 90.
Leicester: Henderson, Stearman, Kenton, Kisnorbo, Maybury (Fryatt 83), Newton, Johnson (Hughes 69), Jarrett, Tiatto (Porter 76), Hume, Hammond.
Subs Not Used: Logan, Johansson.
Booked: Newton, Hume, Kenton, Tiatto.
Goals: Kenton 16, Hammond 58.
Ref: E Ilderton (Tyne & Wear).