Grant scored the only goal of the game after 10 minutes of a physical encounter in Kent.
Elsewhere there was delight for Windsor who beat Combined Counties Premier leaders Walton & Hersham 2-1 and Thatcham Town beat Sevenoaks Town 3-1 at Waterside Park.
The results mean all three remaining Berkshire and Hellenic League sides are in to the fourth round draw which we would expect to be published on Monday at 1pm.
Buildbase FA Vase Third Round
- Lordswood 0-1 Bracknell Town
- Thatcham Town 3-1 Sevenoaks Town
- Walton & Hersham 1-2 Windsor