Longer than anything else except the best available NiMHs (Sanyo blacks) which have the disadvantage (in PBP context) of being rechargeables.
I would take 4 pairs of lithiums (including the pair you start with), and expect/hope to get back with 1 pair unused. Nb 4 pairs of lithiums weighs a mere 120g, which is not very significant compared with say 1 bidon of water. And I would change them at controls - don't mess about with waiting for them to run out mid-leg in the middle of the night.
On a previous PBP, Sheila ran an Etrex Legend Cx for 50 hours on one pair of lithiums. All the way out, and back to Fougeres. The newer Etrexes are a bit more power-hungry though.