The Blues were held to a frustrating 2-2 draw by West Bromwich Albion on Wednesday night to leave Guus Hiddink’s men in 14th place in the Premier League table and 12 points behind fourth-placed Tottenham Hotspur.
Chelsea have struggled to find consistent form this season and their disastrous start to the campaign led to Jose Mourinho’s sacking at the start of December.
The west London side have shown signs of improvement in recent weeks since Hiddink was appointed as Mourinho’s successor until the end of the season.
And former Liverpool man Lawrenson is expecting the home side to have just too much for the Toffees at Stamford Bridge on Saturday afternoon.
Lawrenson told BBC Sport: “Chelsea will probably feel they should have beaten West Brom on Wednesday but Baggies boss Tony Pulis managed to get something out of the game.
“Everton got their draw against Manchester City but this is another tough game for them, and I do not see them holding out again.”
Chelsea, who won the title and the League Cup under Mourinho last season, take on Paris Saint Germain in the last 16 of the Champions League next month.
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