Ok so as the lift is greater, the climb should be greater aswell, right? Or is it just that the lift is greater so the plane can stay up in lower speeds?
to test a theory, my physics teacher taught me to look at an extream case:
a helicopter - is a plane with no wings (no lift) that climbs on it's propeller thrust only, and can stay up at 0 speed.
therefor climb-rate depends on other things as well.
to achive max (sustained) climb-rate, it's easier to consider energy balance. the engine produces energy that is devoured by the drag - what ever is left is going into potential energy - alt (while keeping speed constant).
so to climb at maximum rate you need to fly at a speed that gives minimum drag.
to cut things short, since you are interested in aspect-ratio:
high aspect ratio increaces the efficiency of the wing in high attack-angles (by reducing wingtip turbulance). they will tend to move the "minimum drag" point to a slower speed.
so in general you can say that high aspect-ratio is better for slow speeds / high angles-of-attack flying than a low aspect-ratio of the same area & general shape wing.
there are so many other factors to consider that saying more than that would require writing a book.
Bozon
