The Blues drew 1-1 with Norwich City on Saturday afternoon.
The Blues have one of the most exciting young teams in the Premier League at present, with a number of talented youngsters at their disposal.
John Stones, Ross Barkley, Gerard Deulofeu and Romelu Lukaku have are all currently first team regulars in Roberto Martinez’s side and starring for the team this season.
And Lawrenson says if they can keep those players and help them to grow, then the Toffees can become a very good team in future.
"With John Stones, Romelu Lukaku, Gerard Deulofeu and Ross Barkley, if Everton can keep hold of them and they grow, then they have a real chance of becoming a very good team indeed," he told BBC Sport
“And with Leighton Baines and Seamus Coleman at full-back, is there a better pair in the country?"
With all of their young stars impressing yet again in the Premier League, there is sure to be a lot of interest in their signatures come the summer.
Lukaku will surely be highly coveted, with teams the world over all crying out for a top quality goalscorer and him certainly proving himself among those at present.
Similarly Stones is sure to attract interest again, with Chelsea having already been turned away repeatedly in the summer.
Everton will be confident of keeping them though, with them all secured on long-term deals and more importantly, enjoying life at Goodison Park.
To keep them though, securing Champions League football will surely be key, something that they can definitely aim for this season.