It's not a central part of training, but it's a peripheral part. Lactic acid is technically a misnomer, but I'm sure other people will correct you for that.
Lactate and blood pH are related, but not synonymous. The drop in blood pH during hard running is the result of protons / hydrogen ions / "acid" (H+) being produced when you break down ATP into ADP and phosphate to get energy. This ALWAYS happens when you run fast, no matter whether you are fit or out of shape. The difference is that reforming ATP from spent ADP through the aerobic process (glycolysis plus oxidative phosphorylation) consumes protons, so the net effect is neutral with respect to blood pH. When you rely on anaerobic energy (glycolysis only), there is no mechanism to mop up the extra H+ that is floating around. So even though the conversion of glucose into pyruvate and then into lactate is pH neutral, you haven't addressed the fact that there are protons being dumped into your muscle cells from the breakdown of ATP.
To emphasize, the H+ production from ATP breakdown is non-negotiable - it ALWAYS happens. For the sake of argument, let's set aside running economy for a moment. Let's say we have a 5:00 miler and a 4:00 miler who are the same size and have the same running economy. When they both run 60-sec 400m pace, they both produce the same amount of acid (H+, protons) in their muscles! The main difference is that the 4:00 miler is substantially better at mopping up those protons floating around and using them in the aerobic process to reform ATP. The 5:00 miler does not have the cellular machinery to make that happen, so he relies on glycolysis only to reform ATP fast enough to sustain 60-sec 400m pace. As a result, his blood pH drops much more quickly and he has to stop. This is the MAIN difference between runners of very different fitness levels: the faster runners have a stronger aerobic system. You I'm sure already know how we address this in training: high mileage and high-end aerobic workouts.
Now, with respect to dealing with lactate and blood pH, there are some peripherally important aspects of fitness. Blood pH can be "dealt with" via buffering. Just like you can neutralize vinegar with baking soda, your body uses bicarbonate ions in your blood to buffer against drops in blood pH. This system only works for a little while, though. Lactate itself is also a part of dealing with acidity. If you didn't produce lactate at all, and just let the pyruvate formed during glycolysis float around, you would have your blood pH drop much faster. Forming lactate from pyruvate makes glycolysis pH-neutral, and lactate can "grab onto" a proton from your muscle cell and help transport it out of the cell and into your blood. This helps prevent localized buildup of acidity Lactate itself can also be shuttled around to different places in your body and be burned for energy. We address these aspects of fitness with race-specific interval workouts.
Blood lactate levels and blood pH levels are also not identical - usually they are, but there is a short period where your blood lactate is rising because you're relying heavily on glycolysis to produce energy, but your blood pH has not dropped yet, because your blood buffering system is still churning away, snapping up any stray H+ ions that get dumped into your blood. Soon, the buffering system is overwhelmed and your blood pH drops as your blood lactate rises.
So to answer your question, addressing your ability to "deal with" drops in pH DOES improve your fitness but it is a PERIPHERAL part of fitness. The core problem is how to deal with the inevitable surge of H+ coming from ATP cleavage that is necessary to maintain high speeds, and the answer to this is to improve your aerobic system. Or increase your running economy so you can go faster for the same amount of ATP usage, but that's another story.
This is all addressed in chapter 1 of my book, by the way. It might interest you.
http://www.amazon.com/Modern-Training-Physiology-Long-Distance-Runners/dp/0615790291