When you convert your old site pages over to SLS2, your website lockers are also copied over to the new system. After the conversion is complete, you will have access to the new SLS2 lockers via the Locker tab in the Site Center, but not in via the "My Locker" icon at the top your portal. There, you will continue to see the original website lockers.
Please take note that the old and new website lockers do not stay in sync after the conversion.
If you add or move files to the old website lockers via "My Locker," you will not see those changes reflected in the new website lockers via the Site Center.
Once you publish your SLS2 site, the old website lockers in "My Locker" are replaced with the new website lockers.