The generals appear as bosses at dolmens in a fairly random pattern. Getting and killing all of them will net you the "Daedric Lord Slayer" Achievement and title.
Xbox One - EU - EP/DC
Trying and failing to hold the walls of his Templar house up since 2015
More specifically the lich set only drops from the chest after the lich boss appears.
Draugr Heritage (which I use) drops rarely from other Generals.
Each zone has a set of Generals associated with it, except Cyrodiil where any one of them can appear at a given dolmen.
The below image is Draugr's (including the bow) and some Marksman. Note that most of the armor pieces are called "First Titan" pieces and often get vendored without a player noticing that they even are a Set piece.
Draugr's Heritage set (Knockdown nearby enemies and heal self for 4730 if you are damaged while under 20% Health. This effect can happen once every 20 seconds).
The weapons that drop are only destroy staves, a bow and two-handed axe and maul. Similar 5-piece set bonuses can be gotten from the Apprentice set (Knockdown nearby enemies and heal self if you are damaged while under 35% Health. This effect can happen once every 20 seconds.) and from the crafted Set Death's Wind (If struck by a melee attack while below 35% Health, nearby enemies are knocked back and stunned for 4 seconds. This effect can only happen once every 30 seconds.)
There are 16 generals. None can spawn in your first non-vet zone. So Stonefalls, Auridon, and Glenumbra can't spawn any.
After that, you can break them into four groups of four. The first four will spawn in your second non-vet zone (Deshaan, Stormhaven, or Grahtwood). The second four in your third, and so on.
Once you hit vet content, they can spawn at any vet dolmen. This includes all silver and gold zones, as well as in Cyrodiil. There's no pattern here. You'll get whichever one you get.
So, if you're looking for specific bosses for the achievement, you're better off hunting down dolmens in your non-vet zones, and curb stomping them until you snuff the boss you want. For the drops you're best bet is your gold zones (there's no risk of getting ganked by another player mid-dolmen, and the gear should be 160).