Proper common notation for a ligand
The ACS Style Guide suggests using $\ce{L}$ [1, p. 186] in APPENDIX 10-2 Abbreviations, Acronyms, and Symbols:


  \begin{array}{ll}
[\ldots] &amp; \\
\small{L} &amp; \text{absolute conﬁguration} \\
\mathrm{L} &amp; \text{leucine} \\
 &amp; \text{ligand} \\
 &amp; \text{liter} \\
\mathrm{L_I} &amp; \text {spectral line} \\
[\ldots] &amp;
\end{array}




IUPAC "Green Book" Quantities, units, and symbols in physical chemistry also defines $\ce{L}$ [2, p. 160] in chapter 9 ABBREVIATIONS AND ACRONYMS:


  \begin{array}{ll}
[\ldots] &amp; \\
\mathrm{KS} &amp; \text{Kohn-Sham} \\ \\
\mathrm{L} &amp; \text{ligand} \\
\mathrm{L2TOFMS} &amp; \text {laser desorption laser photoionization time-of-flight mass spectroscopy} \\
[\ldots] &amp;
\end{array}




Glossary of Class Names of Organic Compounds and Reactivity Intermediates Based on Structure (IUPAC Recommendations 1995) uses $\ce{L}$ [3, p. 1349]. For example, see this entry:


  metal-carbyne complexes:
  Metal complexes of the type $\ce{RCML_n}$, ($\ce{M}$ = metal, $\ce{L}$ = ligand) in which formally a carbyne is coordinated to a metal. E.g.
  




$\mathrm{Lig}$ and other notations are not mentioned in the above sources as suitable ligand notations.

Bibliography


The ACS Style Guide: Effective Communication of Scientific Information, 3rd ed.; Coghill, A. M., Garson, L. R.; American Chemical Society; Oxford University Press: Washington, DC; Oxford; New York, 2006. DOI 10.1021/bk-2006-STYG.  
IUPAC “Green Book” Quantities, units, and symbols in physical chemistry, 3rd ed.; Mills, I., Eds.; IUPAC Recommendations; RSC Pub: Cambridge, UK, 2007. ISBN 978-0-85404-433-7.   
Moss, G. P.; Smith, P. A. S.; Tavernier, D. Pure and Applied Chemistry 1995, 67 (8–9), 1307–1375 DOI: 10.1351/pac199567081307.