In short, Gitolite is not able to log a clone or fetch access.
There is a workaround that may work courtesy of Sandeep Kaira.
His email to me after I posted on the gitolite newsgroup:
I noticed that SSL Library records the access to each R/W per user. So, if you install GIT (not gitolite), and give users Git-Shell, then, each of their access is bound to be SSL and will get recorded. The SSL Library will not be able to tell if it is a GIT request or not, but since the user has only git-shell so you can claim that the access was a Git access. You can take backups of these logs (say weekly) if required.
BTW, We went with Akiri Solutions(paid solution). They provide solution around Git (called DevBox) that had some extra features such as “bug management” and “Active Directory/LDAP integration”. Their cost seemed reasonable too. However, they also rely on SSL logs for proof of access.