The Lilywhites head across London looking to continue their recent fine form.
Mauricio Pochettino watched his Spurs side come from a goal down to beat Swansea City 2-1 on Sunday afternoon at White Hart Lane as they secured victory to move three points clear of bitter local rivals Arsenal in the table.
Spurs are currently two points behind leaders Leicester City heading into the final 11 games of the season.
However, former Liverpool man Lawrenson is tipping West Ham to hold Spurs to a 1-1 draw in east London in midweek and deal a blow to their title hopes.
Writing in his column for BBC Sport, Lawrenson said: “A lot of people are looking at Tottenham and thinking they can win the league – and they probably think they can themselves as well.
“But this is a tough game for them because West Ham are not just a skilful side, they are very strong too.”
Tottenham, who finished fifth under Pochettino last season, take on Borussia Dortmund in the last 16 of the Europa League next month.
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