The date applies to the tin too, but you can ignore them relatively safely. Tinned food is sealed inside the tin, and then cooked in the tin at very high temperatures. This kills all the germs in the tin, and as it's a sealed environment no new ones can get in. However, manufacturers have to account for the very low chance that some pathogens survived the heat, hence tins have a sell by date.
Like I said, though, providing the tin remains undamaged and airtight they practically last forever. I should, in the interests of fairness, point out that some brewers swear LME does go off and causes homebrew twang, but given the way the canning process works I don't believe that can be a factor. I'd use it if I were you.
