Translation:This motorway lies between Budapest and Lake Balaton.
On the one hand, a Balaton is how it is frequently called in Hungarian. It is such a significant natural feature that it gets referred to just with the definite article. On the other hand, in English, we very rarely use "The" with the name of a lake. In English, we call it "Lake Balaton." So the answer is: just because that is what this place is called in each language.
For US English an "autopalya" is definitely either an "interstate" or a "freeway", not a highway. "Expressway" is probably also good. As the Szechenyi 2020 infrastructure programme goes forward most of the autopalyak will extend to national borders as well making this an even more apt translation.
We tend to refer to those roads as motorways in the EU. They also have a special sign to differentiate them from other kinds of roads (the one at the bottom here):
Expressways are depicted by the car symbol, they are basically motorways built to lower standards to save money.