Me262 is turbojet fighter, and as such has speed advantage and dive advantage vs La-7. Also firepower is stronger w/ 4x 30mm cannons and good supply of ammunition.

Me262 cannot adjust throttle safely, in rapid combat conditions. Only smaller increments can be added or subtracted of the power setting. Rapid throttle management causes the engines to burst into flames.

On the other hand, La-7 has also quite good speed, good turn and roll rate, good climb rate also... Firepower is also respectable 3x 20mm.

How does the performance change at medium, and high altitudes?

The La7 reaches a peak of power and overall performance at or below 2000m. Engine performance falls off from 2000m up to 4000m then gradually increases power to a true airspeed near 680kph at 6000m. You will need to adjust the pitch, mix, and boost accordingly. The La 7 isnt a high altitude fighter and tends to bleed off energy quickly up hi. The Red Airforce high altitude interceptor was the Mig, that was their plan anyway when the war broke out.

By and large the Red Airforce was a tactical airforce. It fought all it's battles in direct support of the Red Army. Some of their pilots went out with as little a 5 hours training. Besides, the Luftwaffe didnt have much in the way of strategic attack bombers, so the VVS had no reason to develop a counter to it.