The Reds have won their last two Premier League games to keep the pressure on leaders Manchester City.
Liverpool FC were 1-0 winners against Everton in the Merseyside derby last weekend thanks to Divock Origi’s last-minute winner.
Jurgen Klopp’s side dug deep to come from behind to secure a 3-1 win over Burnley on Wednesday night to extend their unbeaten run to 15 games.
Bournemouth ended a three-game losing run on Tuesday night thanks to a 2-1 victory over Huddersfield Town on the south coast.
Eddie Howe’s side have won four times and drawn twice at the Vitality Stadium to sit in eighth place in the Premier League table.
Former Liverpool FC defender Lawrenson is backing the Merseyside outfit to ease to a 2-0 victory over Bournemouth in Saturday’s early kick-off.
“This is a big week for Liverpool, who must win their Champions League group game against Napoli on Tuesday to reach the last 16,” Lawrenson told BBC Sport.
“They can start it by going top of the Premier League if they beat Bournemouth – but only Manchester United and Arsenal have won at Vitality Stadium this season, and neither of them found it particularly straightforward.
“Reds boss Jurgen Klopp made some very brave changes in Wednesday’s win at Burnley, starting the game without any of Roberto Firmino, Sadio Mane or Mohamed Salah up front.
“When they went 1-0 down at Turf Moor, I was thinking ‘this is going to be interesting’ but they responded in the right way.”
Lawrenson added: “Whatever line-up Klopp goes with this time, this will be a test.
“Some of Liverpool’s recent performances have been ordinary, while Bournemouth have been great this season, and returned to winning ways against Huddersfield on Tuesday after losing four in a row.
“The Cherries play good football and are easy on the eye, but they are not a soft touch – and Liverpool will have to play well to beat them.
“I am still really encouraged by Liverpool’s season so far, though – their performances have not been great but, in the Premier League, their results have been.
“In the Champions League, if Klopp’s side had beaten Red Star in Belgrade – and I know it is is a big if – they would be virtually through to the knockout stage already and we would be looking at them in a different light.
“They have not been playing well as a team, but I think what they have done so far is really positive, because I am thinking ‘wow, what will they do if they really get going?’.”
Liverpool FC have won four times in six meetings since Bournemouth’s promotion to the Premier League in 2015.
The Merseyside outfit eased to a 4-0 victory over the Cherries in their last meeting at Vitality Stadium after goals from Philippe Coutinho, Dejan Lovren, Mohamed Salah and Roberto Firmino.
Liverpool FC racked up a 3-0 win against Howe’s side in their most recent Premier League clash at Anfield in April this year.
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