Brown's controversial appointment following the departure of Barry Smith last week has not gone down too well with many of the Dark Blue faithful who are facing the prospect of returning to Irn-Bru First Division next season as they trail St Mirren by 15 points at the bottom of the table.
The former Dundee and Rangers player has shrugged off the negative reaction to his return to the club but knows the focus will be on him in his first game in the dugout, after watching his new charges lose 5-0 to Celtic at Parkhead from the stand.
Saints boss Lomas, though, is looking for his team, fresh from a 1-0 win over St Mirren at the weekend, to keep pressure on second-placed Inverness, whom they trail by just one point.
"We have got to be professional, prepare ourselves right and stick to our game plan," he said.
"We know that Dundee will probably get a lift, teams normally do in those circumstances.
"When a new manager takes over you normally see that in his first game.
"I don't know John Brown but I watched him as a player and he was a very good player, very under-rated and he has great enthusiasm.
"But we can only concentrate on ourselves and what we do."
Lomas does not discount the possibility of Dundee escaping the drop.
"It is possible," he said.
"They still have enough points to play for and they are playing for places in the Scottish Cup quarter-finals, so there is a lot to play for.
"I have watched them in the last two or three months and they have been unlucky in certain games.
"There wasn't much in it when we played them and Hibs were very lucky to beat them at their place.
"They have improved as the season has gone on and they seem to be a lot tighter at the back, so we have to do our jobs.
"We are in a good place, coming off a hard-fought win and it will be the same on Wednesday, it will be another battle."
While Murray Davidson is suspended, fellow midfielder Chris Millar has recovered from a groin injury and skipper Dave Mackay is over an ankle injury and is set to come back in after being on the bench against St Mirren.
The former West Ham and Manchester City midfielder said: "It is good to have the two players back.
"Dave is our captain and he is a seven out of 10 at the very least every week, and often better.
"Chris provides energy in midfield and can play in a few positions so he has been a miss as well.
"So I have a selection dilemma which is nice."