Lumb, who scored his third century of the summer on Friday, settled on 188 from 238 balls before lunch, having hit 24 boundaries, while Wes Durston dismissed Luke Fletcher lbw for 64 from 92 balls.
Nottinghamshire now trail Derbyshire by 39 runs with six wickets remaining.
Sussex survived 11 overs of their second innings without losing a wicket as they attempted to make inroads against Surrey at Arundel.
Openers Luke Wells and Chris Nash added a combined 27 not out, but the hosts still trail Surrey by 126 runs with 10 wickets remaining.
Zander De Bruyn, who reached stumps on Friday on an unbeaten 99, fell to Monty Panesar for 111 with the left-arm spinner also dismissing Zafar Ansari (13).
Chris Jordan completed his three-wicket haul for the innings by removing Gary Wilson, caught by Michael Yardy for 10, and Chris Tremlett, who was pouched by Matt Prior for 54, to end Surrey's stand.