Barnsley have given themselves a fighting chance of Championship survival following a run of four wins in their past eight games, which has seen them lose just twice.
Given that their position looked forlorn when Asbaghi took over in November, it is progress of sorts.
A talisman for their recent upturn has been Morris, who has led the line impressively.
The sight of him leaving the fray with a calf issue with 20 minutes remaining of Tuesday's 2-0 win over Bristol City, when he opened the scoring for the Reds with his second goal in successive games and eighth of the campaign, was the only downside to a positive night and result for Asbaghi's side.
Morris could yet be involved against the Blades if he comes through training today.
Lester, present at Oakwell alongside manager - and former Barnsley chief - Paul Heckingbottom at Oakwell in midweek - said: "I went Tuesday and thought they were quite good.
"They’ve had an upturn, they’re a team we’ve got to be ready for. It’ll be a good game.
"I thought the striker did quite well, I’m looking at where we can hurt them realty.
"Paul and Macca (Stuart McCall) will look at their threats. They’ve got one or two good players, they’re doing better as a team and conceding less big chances and less goals per game since the manager came in.
"We’re looking at them as a team and we think we have enough to hurt them but we have to be wary of their threats.
"We’ve got nine games left, with six at home and we’ve been brilliant at home.
"We’ve got to produce a front-foot positive performance. We’re focusing on ourselves, and with the fans behind us we’re been good at home. We’ll have to find some energy. In a tough session you have one last run before a shower, it’s like that. It’s the last game before a break and it’ll be similar."
John Fleck is being assessed ahead of potential involvement tomorrow, while United are also running the rule over former Liverpool and Derby player Andre Wisdom.
The 28-year-old Leeds-born player, who started his career in Bradford City's academy, is a free agent and on trial.
Lester said: "He's training, and we’ll see how he gets on. He’s been here a couple of days, it’ll be a week or so before a decision is made.
"He’s had a couple of games at Birmingham and was training there, but he’s not had any competitive football.
"It’s not just for a favour, he’s a good player and with the injuries we’ve had across the back we’re looking to add some experience. "And that’s why we’re having a look at him. It depends how well he does, that’ll be down to Hecky and where he sees him long-term."