The Gunners have won the FA Cup in back-to-back seasons thanks to final victories over Hull City and Aston Villa.
Arsene Wenger’s side suffered a setback in their bid to win a first Premier League title since 2004 after a 1-0 loss to Chelsea in north London last weekend.
Burnley, meanwhile, are in third place in the Championship table after a run of four wins in their last five games in the second tier.
Speaking to BBC Sport, Lawrenson expects the FA Cup holders to make light work of Sean Dyche’s side at the Emirates Stadium.
“Burnley are near the top of the Championship, playing really well and scoring lots of goals.
“So I just don’t see Clarets boss Sean Dyche risking too many players at Emirates Stadium when promotion is their priority and they have a chance of an automatic spot.
“Arsenal manager Arsene Wenger will rotate too and, depending on what they need, give people either a run-out or a rest but I would expect to see the holders in the hat for the fifth round.”
Arsenal are three points behind Premier League leaders Leicester City after Diego Costa scored the winner in a 1-0 victory at the Emirates Stadium last weekend.
The Gunners host Southampton at The Emirates on Tuesday night.
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