I am playing my game with LAME installed. I really like all the chnages it does, except how my magicka never depletes to a point where it is an issue. Essentially, I have unending magicka with the regeneration rate too fast.

I can easily fire finger of the mountain incessantly. without causing a appreciable dent to my magicka, as it refills in an instant.

Is there a way to change this, so as to make magicka a limited resource as it was supposed to be in vanilla? Perhaps some mod or a utility that can change this?

I think you've made a small mistake in judgement: LAME doesn't touch Magicka regeneration. The Race Balancing Project does.
The override you're looking for is in the files, not the installation files, folder 07 GMST-Reseters. You'll want bgBalancingVanillaGMSTMagickaRegeneration.esp somewhere in your list after RBP. Unless you use SM, in which case you'll need to edit it's INI to lower the rate instead(as it does it with the INI file, which overrides any mods in your list that edit them, since it calls them from in game).

Hmm no, RBPs magic regen is actually slower than vanilla, if I recall correctly - so using this .esp wouldn't solve the "issue", I think. Editting RBP (or better, creating a patch for it) to tweak this is really easy though - load it in TES4Edit, look for the GMST records, and tweak the 2 or three variables which dictate regeneration. I can't remember exactly which ones right now. But check RBP's readme: the formula is written down there, you'll just have to tweak a setting by a few decimals to change completely the pace.

It's slower with lower wisdom, but faster when it's high enough. Once you pass about 55, it's better then vanilla, and below that, it's slower.

I tried what YX33A suggested, and it seems that I can see magicka not replenishing as fast as earlier, so I am happy. But thanks for pointing that TES4Edit tip to me, Bleral - If the GMST setting is not to my liking, I'll just tweak it with that.

Thanks to both of you!