Using the "L" would put us in good company with almost every "University of" in the country. It takes care of the name law. Additionally, if needed one can easily change the hand sign from UL to L. And, several universities have the same letter reference and are in the same conference, but use a different font to distinguish their brand.
A few examples:
N - Nebraska
N - Nevada
A - Alabama
A - Arkansas
A - Arizona
F - Florida
M - Michigan
M - Minnesota
T - Texas
T - Tennessee
W - Wisconsin