Lee, who won his second European Tour title at the Scottish Open in July, added a 68 to his opening 64 at Marco Simone Golf Club, which will host the Ryder Cup in 2023.
That gave the 23-year-old a halfway total of 10 under par, two shots clear of Fleetwood, Johannes Veerman, Adri Arnaus and Mikko Korhonen.
Fleetwood recovered from a bogey on the 10th, his opening hole of the day, to card six birdies and move to the top of the leaderboard, only to run up a double bogey on his penultimate hole of the day for the second day in succession.
Nevertheless, Europe’s Ryder Cup captain Padraig Harrington will have been delighted to see the world number 38 right into contention heading into the weekend after a consistent, if slightly underwhelming, season to date.
“This year, especially the second half of the year, I feel like I have got off to a good start in quite a few events and then never really kept it going, so today was good,” said Fleetwood, who will be part of Harrington’s European side at Whistling Straits at the end of the month.
“I had spells where I hit it really good and then I had spells where it wasn’t very good, so I guess that is the game, but all in all very happy to turn up after a couple of weeks off and to have a great couple days, and now a weekend with it all to play for.
“Let’s face it, I haven’t played great this year and I haven’t had the year that I want to and every week is the chance to start again in golf, that is the beauty of it.
“I am trying to work hard, I’m trying to get better, and you never know what can turn things around. I’ll just keep turning up, keep trying to do the right things and play.”
Former Open champion Henrik Stenson, who is pushing for a Ryder Cup wild card thanks to a resurgence in form, is three shots off the lead after having to settle for a second round of 71 following a double bogey on the 17th.