They led for most of the second half after Matt Daniel broke the deadlock against Faversham at Culver Road seven minutes after the break.
But D’jean Spencer dashed their hopes of taking all three points with an 87th-minute equaliser.
Lancing are up to 14th in the Isthmian south east table but have no league game until Saturday, November 6, at Burgess Hill.
The Sussex Senior Cup first round kicked off this week and numerous local sides were in action.
Kai Williams and Ollie Hawkins were both on the scoresheet for Arundel but they lost 4-2 at home to Pagham.
But there was better news for East Preston, who won 3-1 at Crowborough.
Harry Margeson scored their first and sub Shane Brazil netted a double.
The county cup also brought another win and another five goals for in-form Littlehampton Town.
Prolific Joe Benn, George Gaskin and Dave Herbert all scored in their 5-2 win against AFC Uckfield at The Sportsfield.
Joining East Preston and Littlehampton in the second round of the cup – at which point the higher ranked clubs join – are Worthing United, who beat Forest Row 2-1.
Most sides return to league action this weekend with Shoreham’s visit to Epsom and Ewell in the SCFL division one among the highlights of the fixture list.