Sturridge scored twice as the Reds beat Tottenham in the EFL Cup, four days after he was an unused substitute in the Premier League against West Brom.
"He is a class act but is not in Liverpool's best 11," said Lawrenson.
"They have Coutinho, Firmino, Lallana, it is just not possible. I think it is a bonus to have him off the bench."
Lawrenson, speaking to BBC Radio 5 live, added: "He is by far and away Liverpool's best goalscorer and he can make himself a goal out of nothing.
"At the moment he doesn't start but no problem, he can come on and score goals and change a game. Why sell him? Why make another team stronger?"
Sturridge, 27, is yet to score in 348 minutes on the pitch in the Premier League this season. He has, however, created two goals and saved his goals for EFL Cup action, with four in two outings.
In four full seasons at Anfield he has hit double figures in the league twice, scoring 10 goals in 2012-13 and 21 the following season.
Liverpool manager Jurgen Klopp acknowledged his player "could have scored three or four" in the win over Spurs but described Sturridge's all-round contribution as "brilliant".
"That's his strength, he's a finisher, a really good striker... no doubt about this," said the German manager, after his side reached the EFL Cup quarter-finals.
"I never was in doubt about him even when he didn't score. Not a question."
Sturridge was one of 11 changes from the side which beat West Brom on Saturday, taking his place in a side which featured a number of youngsters and squad players.
The England international converted from six yards to give Klopp's side the lead and raced clear to add a second having missed a series of chances.
Liverpool striker Daniel Sturridge must show more "bite and fight" to be a first-team regular, according to the club's former defender Mark Lawrenson.