Can I grow Mung lentil sprouts to leaves?

I wouldn’t. At least not when you are talking about true leaves as opposed to cotyledons.

The cotyledons are already part of the embryonic plant and will unfold after the first part of the sprout has reached a certain length. They are perfectly edible in mung beans and contain little or no phytohaemagglutinin (a quick search gave unclear results), which means the sprouts can even be served raw¹, if they were grown cleanly and show no signs of wilting, mold or other spoilage.

I would not recommend trying to get the sprouts past the stage when the cotyledons unfold. The first true leaves need the nutrition stored in the seed and often already the sugars produced by the cotyledons via photosynthesis. If you don’t supply a growth medium light and nutrition, the sprouts are going to starve to death around this time and start rotting.

From a culinary perspective, the true leaves are not a very common kitchen staple, if there’s not a tradition of cooking with them, you may take this as a sign that they are not a desirable ingredient. If your sprouts have started to unfold the cotyledons and are still comparatively light, the sprouts are good. After that stage, the starting photosynthesis will influence the sprouts’ taste and you may find them less desirable, as the flavor gets more bitterish and sometimes musty.

¹ For healthy adults. Recent contamination of commercially produced sprouts show that for sensitive consumers blanching is recommended as safety measure.