Writing in his 'Premier League predictions' piece for BBC Sport, Lawro backed Graham Potter's team to triumph against Garry Monk's Championship play-off chasers.
Albion, who drew 1-1 with Chelsea on New Year's Day, are 14th in the Premier League, while Wednesday have lost their last three league fixtures and are seventh in the league standings.
Lawro said, "Sheffield Wednesday have had a bit of a slump since Christmas, suffering three straight defeats, but I don't think that is any real cause for concern - that is just what it is like in the Championship where lots of teams go on very good runs, then go a few games without a win.
"I would back Brighton to beat them, though, and the Seagulls might fancy a bit of a FA Cup run this year because they have got a bigger squad, and there is a bit of a buzz about the way they are playing under Graham Potter."
Last season Brighton reached the semi-final of the FA Cup and narrowly lost out 1-0 to Manchester City at Wembley.