It only increases the speed threshold before Lather will activate. It indirectly affects stamina consumption because when lathered you consume stamina faster.

Just quick note on your birds stats (derived from your stat maxes). I see you have
4* Stamina
3* Speed, Acceleration, and Endurance
1* Cunning

Cunning does affect the endurance lather threshold in rough terrain. Rough Terrain lowers the threshold and Cunning prevents that. You will definitely want to improve that in your breeding program.
Just an FYI, if you do not have 4* speed, when your bird gets to R300, you will lose very, very often. Finishing 5-7 is normal even for a P9 3* speed bird.