The famous club, formed in 1878 and which has produced more Scotland internationalists than any other, was banished to the bottom of English rugby in 1999 as a punishment for falling into administration.
It has since rebuilt and earned promotion six times in the past nine seasons to be just two steps from the Guinness Premiership, in National League One.
Scottish have continued to confound critics by contesting promotion with favourites Esher to the new second-tier Championship. However, a third defeat in a row at the weekend to tenth-placed Stourbridge has opened up a nine-point gap to Esher, who have three games in hand.
Lynch acknowledged: "With four games to go it is now looking like we'll not make it this season, but Esher have just come down from the Championship and we only just arrived in this league so the team has done very well to be in there challenging, and we're still confident we can finish second.
"The club has really strengthened year on year. We have Tony Copsey now as CEO, who was CEO at Wasps and Harlequins, and he is hugely excited by the potential here; we have The Famous Grouse back on board along with other sponsors, and are developing a professional squad with a top-quality coach in Brett Taylor, and a good team behind him, and good academy and youth squads.
"We are also offering more full-time contracts this year and should have between 12 and 20 full-time players next season. Lewis Calder is the latest young Scot we've signed up. We're also expecting a crowd of between 2,000 and 3,000 for our last home game, against Blackheath, so it's far from doom and gloom.
"If we have to spend another year in National One then fine; that will let us put down more roots, build strength and sustainability and create a stronger package all round."
There remains a possibility of London Scottish going up, and an irony in it, in that London Welsh, Birmingham, Solihull and Coventry have all been struggling with administration this season. But the RFU has changed its policy since the days when Scottish were thrown to the bottom, and now simply deducts points from them.
Lynch added: "We accepted our fate and have just got our heads down and got on with getting the club back on a sound footing and moving upwards again.
"I wouldn't pretend that we would not like the opportunity to step up to the Championship were a club to suffer the way we did, but if there is no fairy with a magic wand this year we will just keep working to ensure that when we do go up we will have the infrastructure to stay there and will not be a one-season wonder."