Lovett-Murray, 28, slightly strained a calf muscle during Friday night's round-robin against the Brisbane Lions and St Kilda, while Welsh, 28, didn't play and is nursing an abdominal strain.
Both will miss this week as "precautionary measures" given the short turnaround between games.
"We've come out of those two games on Friday night pretty well," general manager of football operations Paul Hamilton told essendonfc.com.au on Tuesday.
"Welsh has a minor strain to his abdominal muscle and he will be rested this week pending further advice from club doctors and the medical team.
"But overall, we were quite pleased to come out of those two games with no major injury concerns."
Defender Tayte Pears (ankle) and ruckman David Hille (knee) are recovering well from their respective pre-season complaints but will not face the Demons this week.
"With Tayte, we are treating his recovery conservatively and it is a gradual process because we want to get it right," Hamilton said.
"Tayte is out running and is gradually building up his training, but is still a number of weeks away.
"David is travelling really well at the moment and we are really pleased with his recovery.
"We would hope that we might get a game or two of the NAB Cup into him before the end of the pre-season."
Recent draftee Ariel Steinberg is on track to return to training in the next few weeks as he recovers from the medial ligament injury he sustained in the Bombers' intra-club match two weeks ago.
"In terms of his recovery process, he will need a couple more weeks before he resumes game time but [he] is doing really well in his recovery," Hamilton said.
Andrew Welsh is a $295,600 midfielder in this year’s Toyota AFL Dream Team Competition
