The Hornets visit the Boleyn Ground tomorrow evening.
The Hammers have found themselves in something of a sticky patch at the worst possible time of the season, winning four points from a possible 12 in the Premier League - a run of form which has disrupted their Champions League qualification bid.
In sixth, Slaven Bilic's side sit seven points behind fourth-placed Arsenal and, with five games to go, it appears as if their recent form has put paid to their hopes of finishing in the top four.
Watford have very little to play for but manager Quique Sanchez Flores may have one eye on their FA Cup semi-final at Wembley this weekend, and Lawrenson fancies the Irons as a result of the Hornets potentially preserving their best players.
"I was very impressed by West Ham when I watched them draw against Leicester at the King Power Stadium on Sunday," he said to BBC Sport. "The Hammers really should have won the game - if you are going to award penalties like the one Leicester got in the last minute, then there are going to be 10 a game.
"West Ham don't stop coming at you, they are very physical and strong, and they have got different ways of scoring. Watford ended their six-game winless run in the league by beating West Brom on Saturday, although they were a little bit fortunate with the Baggies missing two penalties.
"With the Hornets playing Crystal Palace in the FA Cup semi-finals this weekend, their manager Quique Sanchez Flores is going to change his team around. Because of that, I am backing West Ham."
Victory would see them apply the pressure on the Gunners - who face West Brom on Thursday - but more dropped points may spell the end of the Hammers' Champions League dream.