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I can't speak for other chemistries, but in the flooded lead-acid ForkenSwift, it gets slower as charge is depleted.
To be more specific, the battery voltage sags more under load when the charge is low, and if you push the car hard and pull the batteries under 5.25v (per batt) under load, you can damage them.
When you say the forklift works well until the last bar, that tells me you're probably seeing an engineered display which is meant to protect the batteries (ie. the last charge bar goes out well before you're actually in danger of damaging the pack). That would explain why you don't see a massive performance drop at that last bar.
Modern, production EV's will likely have electronic protection that prevents you from draining the pack so far as to seriously hurt acceleration and/or damage the pack. (They'll also come with something other than lead acid chemistry, which may have better performance characteristics as the charge is depleted.)
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