When searching for Dragon cards, different Dragon Spirits came up as part of the selection, but that may just have been part of the keyword search. So I'd just like to clarify things with "yes Dragon Spirits will trigger her ability" or "no, it won't"
Yes, Lathliss's ability will trigger from any creature with "Dragon" in the type line, including Dragon Spirits like Kokusho.
Each word of the type line is a separate type that is treated independently. So when you look at a card with "Dragon Spirit" in the subtype, you do not threat that as a single unit, it means that it is both a Dragon and a Spirit. This is stated in rule 205.3b:
Subtypes of each card type except plane are always single words and are listed after a long dash. Each word after the dash is a separate subtype; such objects may have multiple types. [...]