The film has seven nods in total including Colin Farrell for best actor and Olivia Colman and Ben Whishaw for their supporting roles.
Marital drama 45 Years and Macbeth have six nominations each.
The winners will be announced at a ceremony at London's Old Billingsgate on Sunday 6 December.
Yorgos Lanthimos' The Lobster is also up for best British independent film, best director, best screenplay and producer of the year.
Set in a world where singledom is forbidden, anyone not in a couple checks into a hotel where they have 45 days to find a mate or they are transformed into an animal.
Alongside The Lobster on the best British independent film shortlist are 45 Years, Amy Winehouse documentary Amy, sci-fi thriller Ex Machina and Macbeth.
Amy, Brooklyn and Ex Machina all have five nominations each.
Both Charlotte Rampling and Tom Courtenay received acting nominations for their lead roles 45 Years, while Marion Cotillard and Michael Fassbender were similarly recognised for Macbeth.
Carey Mulligan, Helena Bonham Carter and Anne-Marie Duff are all nominated for their performances in Suffragette.
Alicia Vikander is nominated for best actress for The Danish Girl, while Tom Hardy is nominated for best actor for his performance as both Kray twins in Legend.
As previously announced, Kate Winslet will be presented with the Variety Award, which recognises a director, actor, writer or producer who has made a global impact and helped to focus the international spotlight on the UK.
The full list of nominations is on the Bifa website.
Surreal dystopian drama The Lobster tops the list of nominations for this year's Moet British Independent Film Awards.