The term "lynching" originated in the late 1700's, around the time of the American Revolution and is believed to have originated in the US. This show is set in the early 1600's, almost a century and half too early.
D'Artagnan remarks that when the musketeers would be caught in disguise, they would be executed as spies. Apart from the fact that their 'soft leather harnesses in all kinds of shades and shapes' hardly look like a decent uniform (mousquetaires de la garde wore colourful white-red-blue uniforms), it was only at the first Hague convention (1899) that a sharp distinction between the treatment of combatants with and without proper uniform was discussed (and only included.in the second convention of 1907). Before that, the exact garment of a soldier was not that crucial.
Moreover, the musketeers weren't spying either (clandestine intelligence gathering), neither on a sabotage mission - acts and goals that would outweigh what they wore.
And given the amount of violence and shooting, d'Artagnan's worry about a possible execution seems trivial.
The anachronistic remark only serves to show how much he likes his team colours and is reluctant to shed them, even for tactical reasons.
Moreover, the musketeers weren't spying either (clandestine intelligence gathering), neither on a sabotage mission - acts and goals that would outweigh what they wore.
And given the amount of violence and shooting, d'Artagnan's worry about a possible execution seems trivial.
The anachronistic remark only serves to show how much he likes his team colours and is reluctant to shed them, even for tactical reasons.
When D'Artagnan is swimming through the tunnel he struggles for breath as he tries to loosen the bar of the underwater gate, however there is a small gap at the top of the tunnel, meaning he would not have to struggle for breath.