I think the Lot département would have little influence on the route anyway - its participation would have been in the name of the general benefit to the region (it is one of the départements of Midi-Pyrénées).

The third public consultation on the route started recently, as you say. There are a number of points of local friction - north of Toulouse, for instance, or at Agen. The kind of problem that usually ends up getting fixed.

But the PPP financing with Vinci comes in for more and more criticism. Vinci is pushing the envelope up to €8bn, more than the Tours-Bordeaux section. At the same time, the State claims not to have the means to finance directly.

From the (April) newsletter of the Europe Ecologie-Les Verts representatives on the Midi-Pyrénées regional council:

Voici des mois que les élu-es régionaux Europe Ecologie Les Verts défendent la liaison Paris-Bordeaux-Toulouse en TGV par le réaménagement des lignes existantes, notamment parce que le financement du projet en partenariat public privé apparaissait complètement irréaliste. L'actualité de la semaine vient conforter la position des écologistes : le TGV n'arrivera jamais à Toulouse si les différentes parties prenantes s'obstinent à croire qu'il est possible de réaliser un projet alors que de plus en plus de collectivités se désengagent, que RFF tire le signal d'alarme, que Vinci réclame à RFF 60 millions d'euros supplémentaires faisant ainsi exploser la facture au delà des 8 milliards d'euros...

For months now the regional representatives of EE-les Verts have been supporting the Paris-Bordeaux-Toulouse TGV connection by conversion of the existing lines, notably because the project finance by PPP seems completely unrealistic. This week's news [the Lot pulling out] backs up the ecologists' position: the TGV will never reach Toulouse if the different stakeholders obstinately go on believing it is possible to complete a project while more and more local authorities pull out, while RFF sends alarm signals [about financing], and Vinci demands €60mn more from RFF, pumping up the bill to over €8bn...

EE-les Verts argue their position in favour of a cheaper project (at 220 kph), in this pdf (in French).