My experience, and it is considerable, is that the La-7 turns well enough to be a threat to most fighters in a low-speed maneuvering fight. The problem most people encounter is that they are flying the La-7 too fast to take advantage of it's maneuverability. Another factor is the La-7's outstanding rate of turn. It can get around a slightly bigger circle faster than many better turning fighters can get around their smaller circle. Bighorn and I demonstrated this with me flying an F6F and Bighorn flying the La-7. I could easily turn inside the La-7, but due to the Lavochkin's much higher rate of turn, I could not gain enough to pull lead for a shot. Worse, the La-7 was able to get the nose up enough to gradually gain an altitude advantage, whereupon Bighorn would break from the circle, unload and accelerate away. This allowed the La-7 to extend out enough to reverse into another merge, resetting the fight. Then there is the La-7's significant advantage in WEP duration. This means that I had to use my WEP sparingly. The net result was that neither pilot could get an advantage on the other that was sustainable long enough to count.
That said, the fact remains that the Spit XVI owns the La-7 in every category but speed. Likewise, the Spit VIII is a little slower yet than the XVI down low, but matches it in climb and acceleration. The XVI rolls faster, but the VIII is more stable at high angles of attack. Which means that the VIII will wear down the XVI in a protracted stall-fight. Equal pilots, both the Spit XVI and VIII should triumph over the La-7 in a maneuver fight. Adding to the La-7's woes is the Spitfire's Hizzooka cannons, with far superior ballistics.
Another fighter that will give the La-7 fits is the 109G-2. Clean, they are about equal. Slow, the 109's far better flaps give it the edge. However, the 109 pilot must remember to NEVER attempt to reverse to the right with flaps out at low-speed. The 109 simply will not roll right, even with full right rudder, unless you pull off power to minimize the torque effect. Rolling right takes too much time and the La-7 will quickly gain the advantage. Pulling back power means having to get the nose down to avoid a stall... Another thing you don't want to do. So, keep going left no matter what. Knowing your aircraft and fighting it the way it fights best is always a very important aspect of air to air combat.
If you believe the La-7 is not exceptionally maneuverable, think again. Go to the TA, practice flying it to it's limits. Learn where it's strengths lie and it's weaknesses are. Then, fly to the strengths and avoid the weaknesses.