In practice, the lyophilised solid is far more robust than anything anyone says about it, and the solution is far less robust. Most of the confusion in this area comes from advice about one being applied to the other.
For the solid state, residual moisture is the dominant variable. A cake at two per cent water is considerably more stable than the same cake at six per cent, because water is both a reactant in hydrolysis and a plasticiser that lowers the glass transition temperature. This is why a desiccant in the outer packaging is not theatre, and why opening a cold vial in a humid room is a genuine error — you condense water onto the cake.
Practical thermal arithmetic for a shipment: a single 250 g phase-change pack in a thin-walled polystyrene box holds sub-ten-degrees for roughly 24 to 48 hours in a 25 °C ambient, and considerably less at 35 °C. Any lane taking eight to fourteen days is therefore not temperature-controlled for most of its duration regardless of what was in the box, which is the argument for shipping the material lyophilised.
General guidance on lyophilised peptide storage from the major synthesis houses converges on minus twenty degrees for long-term storage of solids and refrigerated storage for solutions in use, with the explicit note that repeated freeze-thaw of solutions should be avoided. It is consistent advice precisely because it follows from the chemistry rather than from a study.
Worth stating: research-use-only material has no stability programme behind it at all, so any beyond-use date you apply is your own construct.
The single highest-value change most people can make is buying a cheap logging thermometer, because it converts an assumption about their storage into a record.