The maillot here refers to le maillot jaune, which in cycling event Le Tour de France is awarded to the currently leading competitor (in matter of time).

Knowing that, the expression prêt à lâcher son maillot can be translated to ready to (give up/lose) his (leading position/leader status).

The full expression is “lâcher son maillot jaune” and it is used only in the context of the Tour de France.

It means dropping out from the first place and thus giving one’s own yellow jacket up to another racer.