You will not find a symmetrical "L". However, you could go for lowercase (but then, it would be very narrow.
You could try with an upside-down "T".

Vertically, as in stacked or rotated 90 degrees?

With a slab, it might be easier to optically center the L because you can counteract it's asymmetry with a heavy serif. Also a monospaced font might be worth trying, and also a grotesque of some kind because they usually have rather uniform widths in the capitals. All suggestions for stacking. Rotating is another story. I highly suggest you consider employing some of thetalent lurking around here. Most of the long timers are type designers that would be able to produce a tailor-made product for your needs.

The problem I have noticed is with the 'M'(and sometimes 'N' also) as its width is visibly more than the other letters in the word. Considering squishing it. But if you know of any font/s that already have all 'same width' letters, pls name them.

Monospaced fonts at FontShop