Like everyone said your way to tell if it's an LB7 or LLY is by the vin.
Other things to look for are typical silverado problems
-rattling steering shaft
-check ALL of the front end joints i.e. ball joints, tie rods, pitman arm, steering arm, cv's
-Look for seal leaks especially the axle seals on the front diff as they like to wear out faster than recommended replacement
-Check out the brake lines for large amounts of rust.
Other major problems to look for are related to either lly or lb7
LB7:
-Find out if injectors have been done
-If they have been get paperwork, when were they done, were they reman'd injectors or brand new? (also remember just as with any diesel just because they were done or done recently doesn't mean they won't go bad the next time you drive it)
LLY:
-injector harness inspection as they are known to have problems
-see if it still has the stock mouthpeice or if it has already been swtiched to an LBZ mouthpeice or aftermarket. (if it has you know the current or one of the previous owners may actually care about the truck and preventing problems)
And always inspect the trans operation and fluid (level, smell, and visual)
-This is another thing that on any vehicle though just because it's mint now doesn't mean something can't go wrong the next time you turn the key. That's any vehicle though bud not just a duramax.
Good Luck!