Lactic Acid does not cause arthritis per se, as a direct connection. 

Lactic Acid can build up, for example, when you have exercised past your body's tolerance.  The way to check is to try to speak while you are exercising; if you cannot carry on a simple conversation, you should take a break.  

If you are referring to the general influence of acid on arthritic joints, there is a connection between nutrition and the worsening of arthritic pain.  The Nightshade group of plants (tomatoes, eggplant, green pepper, white potatoes, caffein) should be avoided; drink water on a regular basis, and keep the area of arthritis warm and moving.