“Using oxygen more efficiently is probably a poor description”.
If your lactate threshold occurs at 70% of Vo2 max and then improves to occur at 80% of max (VO2 max remains constant) then what happened? Is it running efficiency by improving your skills? No, running efficiency would decrease the amount of O2 used at a given pace. So, your lactate threshold PACE would improve, but that’s not what we’re talking about. We’re talking about percentage of VO2 max.
Let’s say VO2 max is 100 somehow. Why are you now able to use 80 ml/kg/min of O2 at your threshold when previously you could only use 70? Well, probably for the same reason people use sodium bicarbonate and beta-Alanine (or topical carnosine). Your buffering abilities become better. There are also enzymes that shuttle lactate both in and out of the cells so it can be recycled faster. Maybe your ability to exhale CO2 to increase pH gets better (I just made the last part up- don’t know if that really happens).
You are always producing some lactate and H+ ions. So for some people, at 70% VO2 max, the amount of lactate and H+ becomes more than what their body can process and recycle (or get rid of). So lactate levels start to rapidly rise and many call that the “threshold”. But then, you get better at buffering and recycling (for example muscle carnosine levels increase, your enzymes change (I’m forgetting them- LDH, MCT-1, MCT-4??) and basically now you can produce more lactate and H+ (the amount you produce at 80%) without the levels rising. It’s like if you’re filling up a bathtub with the drain open- the water levels will start to rise when the amount of water coming in, exceeds the amount of water draining out. If you get a bigger drain, it will take more water coming in for water levels to rise. (Not a perfect analogy because lactate doesn’t leave- it gets recycled, and you also have H+ and overall pH which can also be increased by getting rid of CO2… but some CO2 is also important for optimal O2 uptake by the muscle … not to mention we always measure blood lactate… but that’s not always 100% accurately describing what’s going on in the muscle.. anyways there’s a lot going on all at once unlike the bathtub)
*This is all based on recall from some basic Google searches about 7 years ago. So, my knowledge is about equivalent to a 2nd grader. So take this with an extra small grain of salt.