The former defender says there are no characters like Steven Gerrard or Jamie Carragher and the squad is "playing for themselves".
The Reds were beaten 3-1 by Manchester United on Saturday in a poor display that has left many questioning where they are heading as a side.
They lost long serving captain Steven Gerrard this summer as he headed to the MLS with La Galaxy, while his replacement as captain, Jordan Henderson, missed the trip to Old Trafford through injury.
And Lawrenson says the biggest problem for his old side is the lack of leaders in the side.
“The biggest thing for me is that they are characterless,” he told Match of the Day 2 Extra.
“There’s nobody there saying ‘what’s happening', they are leaderless. That for me is the biggest problem, there’s not a Carragher or a Gerrard. Somebody who will help other people on the pitch, they’re all playing for themselves.”
Lack of width a big problem
The former defender has also expressed his concerns over the lack of width in the side.
Brendan Rodgers was busy this summer as he brought in a number of players following a disappointing campaign although none of those were wingers.
Currently youngster Jordon Ibe is the only out and out winger in the squad after they allowed Lazar Markovic to head out on loan. And Lawrenson says their lack of width is an issue but the West Ham loss was a bigger one than the United defeat.
“I think in all honesty the worst defeat for Liverpool was West Ham, it was such an inept performance,” he added.
“A big thing for me is that they are just so narrow. You’re looking at Liverpool at the moment, there’s no width and they don’t create too many opportunities..”