Joe Bennett and Joe Clarke got the Lions' goals at Culver Road to keep up their 100 per cent winning start.
Boss Kerry Hardwell said: "I was delighted to get another three points. After a frustrating afternoon against Steyning on Saturday where we weren’t anywhere near our best, I told the boys we’d all need to raise our game to get anything from last night's game - and the boys certainly did that.
"They listened to the instruction we provided to them. We were compact throughout and all 15 players that played really did put in a shift.
"Lancing move the ball very well on the Sussex county pitch but rarely troubled Connor Kelly in goal. We should really have been out of sight at half-time after having three great opportunities.
"We went ahead on the hour mark from a great header from Joe Bennett, however five minutes later we have didn’t retain the ball well enough and got punished.
"But on 80 minutes Joe Clarke burst through and fired home under the Lancing goalkeeper. If we’d have left there with just a point last night I’d have been disappointed so I was delighted with all three.
Pagham host East Preston on Saturday 12:30pm)
Wick O Worthing United 2
Two goals in the first 15 minutes condemned Wick to defeat in Tuesday’s Southern Combination Supplementary Shield match with Division One rivals Worthing United.
Alert Mavericks striker Danny Hills pounced on a mix-up in the Dragons defence to put the visitors ahead after just 20 seconds. Then Hills was brought down by Wick goalkeeper Lewis Boughton in the hosts’ penalty area and Callum Thoms made no mistake from the spot.
Worthing, led by the impressive James Thurgar, worked hard to prevent Wick getting back into the game and it was all over when Josh Clack saw red after retaliating when he was chopped down in the 56th minute.