The Gunners had a bid rejected for the France international, 26, but talks have progressed and will continue over the coming days.
Lacazette's move is expected to be for a club-record fee, surpassing the £42.4m paid to Real Madrid for Mesut Ozil in 2013.
However, a deal for Monaco midfielder Thomas Lemar, 21, is less likely after a bid was turned down. Meanwhile, Arsenal have not yet received any bids for 28-year-old Chile forward Alexis Sanchez, who told reporters on Friday that he has made a decision on his future.
Speaking before his country's Confederations Cup final against Germany on Sunday, Sanchez told reporters: "I'm clear, but I still can not tell you."
Sanchez only has a year left on his contract and Arsenal still hope he signs a new deal.
However, if he opts not to, the Gunners may be willing to sell him rather than letting him leave for free next summer.On Thursday, Gunners chief executive Ivan Gazidis promised fans "top quality" summer signings during a question and answer session.
So far this summer, left-back Sead Kolasinac's is the only recruit, joining from Schalke.
Lacazette, who has 11 caps for France, has been linked with several top clubs and looked set to join Atletico Madrid prior to their transfer ban being upheld by the Court of Arbitration for Sport.
He broke into Lyon's first team during the 2009-10 season after a successful time in the youth setup and has since scored 129 goals in 275 matches in all competitions.
Last season was his most prolific as he found the net 28 times in Ligue 1, a tally bettered by only Paris St-Germain's Edinson Cavani, with 35.