I'm interested in what the primary climate would most likely be in the pictured region, especially between the two latitude lines (35N and 40N). Does having something similar to the midwest US (from about Tennessee through the great lakes, just east of the Mississippi river) make sense?
World details This planet is roughly earthlike for the purposes of this question. There are small differences, but they're within 0.5% or so of Earth norms as far as radius, distance from sun, insolation, inclination, etc.
Regional details Despite the very non-tectonic origins of the landforms/mountain ranges/etc, the weather processes since their formation (in the distant past) can be approximated (at least for this question) as earth-like.
Mean altitudes are noted, although there's variation. Specifically, the main plains region east of the lake rises slowly from roughly sea level at lakeshore up to 300m or so before the mountains start. The ring-shaped mountain ranges (outer and inner) are roughly 70 mi (+- a fair amount) wide. This makes them quite steep and sheer throughout much of their length.
The lake is freshwater, but the sea to the north is salt (part of a much larger ocean stretching to polar regions). There are outlets to the lake, but they're not shown on this map. The sea to the south is part of an equatorial sea stretching through the northern tropical and subtropical regions and extending across the entire east-west length of the continent.
To the west of the lake is another large plains region of approximately the same extent as the eastern one and another rugged mountain range (similar to the Rocky Mountains in the US). Beyond that is an ocean similar in extent to the Pacific. To the east of the pictured region is another few thousand miles of terrain, mostly fairly arid at least close by.
Tree cover is sparse in the plains by the lake but in the southern inter-mountain region it's fairly dense. The mountains (at least the lower slopes) and hills of the north and east are forested. The northern intermountain region (around where it says +450 m) is, ideally, basically badlands, as long as that makes sense.