On my option list printout I can't find a specific LSD option but it has the p30 " performance pack". And one called "rear axle " which isn't very specific??
His - Denim Blue A220 AMG Line Premium / Hers - Obsidian Black R172 SLK55
The reason I ask is that my 2012 E63 is a Performance Package Plus version, and on the OASIS report it lists both Code P30 "AMG Performance Package Plus" which in the sales blurb includes the LSD, and Code 471, "AMG rear axle limited-slip differential lock", so I'd expect the C63 report to list Code 471 if it's fitted with an LSD.
You could also tell by switching off the traction control, selecting 1st gear and standing on the throttle. If you get a nice even number 11 left on the tarmac, it's fitted with an LSD
Yes it's still 471 with a c63. It is confusing. A lot of sellers (private or even main dealer) genuinely think if it a PP or a PPP car that it's got lsd. Not the case I'm afraid even with the early c63's.