Lacazette's contract is up next year and several clubs including Serie A side Roma and Spanish team Atletico Madrid have been linked with moves for him.
Arsenal's realistic hopes of Champions League football next season now hinge on success in the Europa League as they are nine points adrift of the top four down in ninth.
On a costly afternoon for Spurs' hopes of a top-four finish, Tottenham also lost Son Heung-min to a hamstring injury at the Emirates, while Lamela went from hero to villain for the visitors with a needless second-half red card.
Premier League: Arsenal impress with comeback win against Leicester, Gareth Bale stars as Tottenham beat Burnley
The defeat left Leicester in third place, trailing leaders Manchester City by 13 points with 12 games remaining.
Premier League: Son Heung-min nets 100th Spurs goal as they defeat Leeds; Arsenal register third successive win
Son grabbed the second goal for Jose Mourinho's side after Harry Kane's penalty had opened the scoring at the Tottenham Hotspur Stadium.
Marcus Rashford's 93rd minute strike beat Wolves 1-0 to move Manchester United into second in the Premier League. Leeds, meanwhile, thrashed West Brom 5-0.
A first league victory in nearly two months was vital, therefore, to boost Arsenal players' fragile confidence — even if it only lifted them into 14th place.
Arsenal fans Steve Manzanero recovered from the coronavirus last month but sees fans returning as a necessary part in the reopening of society.
Premier League: Jamie Vardy seals victory for Leicester against Arsenal; Wolves, Newcastle share points
Arsenal are languishing in 10th after a second consecutive league loss following their 1-0 defeat at Manchester City last weekend.
Ahead of the FA Cup match against Manchester City, Arteta said: 'I see how he’s training every day and know that he’s happy.'
Premier League: Leicester's top four hopes under threat after loss to Bournemouth; Tottenham win north London derby
A 4-1 capitulation at relegation-threatened Bournemouth on Sunday summed up Leicester's form since the Premier League returned from its three-month coronavirus-enforced shutdown.
A video emerged online where Alexandre Lacazette could be seen inhaling gas from a balloon
Coronavirus Outbreak: Alexandre Lacazette, David Luiz among players spotted in action as Arsenal reopens training ground
France striker Alexandre Lacazette, Brazil defender David Luiz and Switzerland midfielder Granit Xhaka were seen arriving at the Arsenal facility, which is situated 20 miles north of London
Premier League: Liverpool recover from early scare to beat Bournemouth; super-sub Alexander Lacazette scores as Arsenal win
A scare survived this time, and Liverpool moved closer to lifting the Premier League trophy.
FA Cup: Arsenal beat Leeds to set up fourth-round Bournemouth clash; Manchester City, Liverpool to face lower-tier teams
Leeds out-shot Arsenal 15-3 and dominated possession in the first half and demonstrated why Marcelo Bielsa's side is well placed to end a 16-year exile from the Premier League
Premier League: Arsenal endure worst run since 1977 with Brighton defeat; Newcastle beat Sheffield United
Arsenal slumped to a 2-1 home loss to Brighton in the Premier League on Thursday, taking the team's winless streak to nine games in all competitions — their worst run in 42 years.
Premier League: Arsenal strip Granit Xhaka of captaincy over outburst; Pierre-Emerick Aubameyang to take over role
Arsenal manager Unai Emery confirmed on Tuesday that Granit Xhaka has been stripped of the club captaincy after an emotional outburst towards supporters.
Premier League: Arsenal manager Unai Emery defends 'mature, experienced' Granit Xhaka after naming him permanent skipper
Xhaka, 27, has been fiercely criticised for his performances since joining the club in 2016 and was booed off by Arsenal fans when he was substituted during last weekend's clash with Aston Villa.
Premier League: Arsenal striker Alexandre Lacazette sidelined until October due to persistent ankle injury
Lacazette had been playing with pain from the problem for several weeks and the France international has now been told to rest in the hope it will allow time for the problem to heal
Premier League: Spurs' Harry Kane slams reports claiming he dived on purpose to win late penalty against Arsenal in London derby
Kane had already scored a first-half penalty after Granit Xhaka's foul on Son Heung-min, giving him 10 career goals in north London derbies