The 28-year-old Scot failed to find the net for the Lilywhites in 10 appearances in the second half of the 2010 season but finally broke his Oriel Park duck in the 77th minute to earn Heimir Guðjónsson's side a share of the spoils.
Bodvar Bodvarsson's cross from the left was only partially cut out by Paddy Barrett, with Lennon on hand to slam to the bottom left hand corner past a helpless Gary Rogers.
It looked as though Stephen Kenny's side were going to claim a famous win when David McMillan gave them the lead 11 minutes earlier.
Full back Sean Gannon released Patrick McEleney on the right and his inch-perfect cross was met by the inrushing McMillan, who slotted home first time past Gunnar Nielsen to the bottom left hand corner.
The 27-year-old had earlier squandered the Louth men's best chance in a first half which they just about shaded.
A minute before the break Daryl Horgan's free kick was parried by Nielsen with the rebound falling to McMillan, who fired over from six yards out.
FH had earlier gone close themselves on 27 minutes when Atli Gudnason forced a fine stop from Rogers.
Lennon's late goal was a huge blow to a Dundalk side who dominated for the most part and restricted the visitors to few chances but they will be confident they can still advance when they travel to Iceland next week.
Rogers; Gannon. Gartland (Barrett 43) Boyle, Massey; Mountney (Benson 81), Finn, O'Donnell, Horgan; McEleney; McMillan (Kilduff 78). Subs not used: Shields, Grimes, Meenan, Sava.
Nielsen; Hendrickx, Doumbia, Olafsson, Bodvarsson; D Vidarsson (P Vidarsson 87), Pálsson, B Vidarsson; Valdimarsson, Lennon, Gudnason. Subs not used: Hewson, Nattestad, Bjornsson, Swerwy, Gudmundsson, Finnbogason.
N Popov (Bulgaria)