After losing their first-choice half-backs pairing in MacGinty and Randall, plus top-try scorer of last season Ibitoye, in the first match of the season against Leicester, Bristol then lost back Tom Jordan (a wrist knock that has since recovered), centre Joe Jenkins and wing Rees-Zammit in the defeat by Saracens on Saturday.
Bristol are also without Noah Heward, Rich Lane, Will Capon and Max Lahiff and next face Exeter on 11 October.
“We only named the team [on Thursday] and had one training session because we had 15 backs unavailable, which is never heard of before,” Lam told BBC Radio Bristol.
Jordan is said to be “looking OK” but Wales’ Rees-Zammit will be out for weeks.
However, Lam said his time on the sidelines will “hopefully not [be] long” and that he would feature for the team before the autumn internationals begin next month.
“We’re hopeful, he’s hopeful and we’ll see what these few days [are like],” Lam said.
“He was struggling to walk after the game, he’s in a moon boot currently.”
Jenkins, however, is to have surgery and be out until 2026 due to a “proximal hamstring rupture”, after his foot got caught as he was cleared out at a breakdown.
“We’ve got a lot of backs in the squad but we can’t get over how many are injured,” Lam said.
One boost is the Bears have prop Ellis Genge available for the first time this campaign following his return from the British & Lions tour, as well as Argentine trio Benjamin Elizalde, Pedro Rubiolo and Santiago Grondona who have returned following the Rugby Championship.
