Are you assuming eqaul pilot ability? Most often it is not, and its the pilot that wins the engagement not the plane.
The aircraft are fairly similar in ability, but the sustained turn advantage goes to the spitty (but all but equal with flaps out). But from my testing, HTCs charts, and Gonzo's little app
http://www.gonzoville.com/charts/index.phpThe La-7 holds some adavantages - for example speed (quite a bit) , high-speed acceleration, climb without WEP (under 7k), firing time, it also has 3 nose-mounted cannons (no convergence issues).
I wouldnt assume the La-7 is done for by any stretch. The biggest determinant would be pilot ability. If you take that out (can you practically??) then if it turned into a series of slow speed turns and vert manuevers the spit would probably eventually win if the La didnt extend. But thats the La playing away from its strengths into the spits.
If you took the other approach and the La played to its strengths of staying very fast, staying low, and using a series of attack (and i dont necessarily mean HO) extend, repeat style of fighting, then you should be able to wear the spit down and kill it. Use your speed to zoom higher (either out of range or roping) and reverse back keeping the spit turning as you put the pressure on him to keep turning hard (his strength) to chase you.
Or you could mix it up, faint by doing a few attack-and-extends, but on the third or so, lead turn and go for the jugular and catch the spit out, he may not expect the La to turn so aggressively. Sometimes it works...
But hey, im no La7 pilot. They're no challenge to me.