To me Old School is exploration based play where player skill is tested. It has a certain feel to it. I know I can do it with 3e rules, so it's not the rules. I probably could do it with 4e or 5e if I cared to learn new rules sets.
For me I don't consider Dragon Lance the end of the Old School, but the culmination of it. If you look at modules like Ravenloft, Pharoah, and Dragons of Flame they are still exploration based. You have stories built into them, but those stories are meant to be played out principally in the geography of a dungeon.
The module is king in Old School, and the module is fundamentally in Old School a keyed map. You've seen those big posters where it tracks some party's path and misadventures through a dungeon? If you can't do that, then it isn't old school.
The end of the Old School is marked by the introduction of Forgotten Realms, and the attempt to recapture the magic of DL by focusing on the living out the story of the novel part of DL if you took the narrative short cuts in DL at face value and took Krynn itself and not the adventure as the thing that was really interesting and worthwhile. I'd mark the publication of Shadowdale in 1989 as the end of the Old School, though really there is a gray period here so that if you didn't play before 1986 you probably never experienced old school except second hand via a DM that did cut his chops before 1986. The TSR modules beginning around 1989 have a very different feel to them for the most part. Second edition would eventually lose interest in modules and acquire a focus on this massive canonical settings like Forgotten Realms, Dark Sun, and Planescape and that marks the Silver Age, but by that point we are already in new style of gaming with a very different set of focuses.
The new school is marked by a focus on something other than the adventure, and the adventure is usually something other than exploration based.