The Lions, who had only taken one point from their opening four games, looked on course when midfielder Martyn Woolford drove them ahead shortly after the break at the Amex Stadium.
But Dunne, booked earlier for time wasting, received a second yellow card for a foul on substitute Andrea Orlandi before Argentinian striker Leonardo Ulloa rescued a point for the Seagulls a minute from time.
Dunne's dismissal was hard for Lomas to take, especially as he predicted it could be coming at half-time given the nature of the first yellow card.
"I said to the fourth official that it was a very cheap booking and I could see what could happen in the second half," Lomas said.
"The sending off was definitely the key part of the game and the turning point as we were comfortable.
"We set up to nullify Brighton, who we gave due respect to after they won their previous two games.
"We deserved our goal and to come away with a draw is disappointing really because the players were superb."
With Monday night's transfer deadline looming, Lomas stressed the need to "inject fresh blood into the squad".
He said: "I believe that if we are to really, truly take this great club forward we need some fresh blood and there needs to be an injection of new faces.
"Too many players have become stale. Hopefully we can shift a few on and be creative."
- Sports & Recreation
- Leonardo Ulloa