Although the Lakota can build in neutral territory, for the neutral territory near a city under assimilation, they can only build a City or Fort and not other buildings (such as Towers). This allows the Lakota to build a Fort right next to a captured city even while it's still being assimilated.
The Lakota can build Towers and many other buildings anywhere in non-enemy territory on a new continent (similar to if a nation's territory extends to the new continent), but still needs Commerce 2 (Coinage) to build a City or Fort on a new continent. The limit to being near the coast for the first City or Fort also still applies.
The Lakota unique Ranged Cavalry have 33 movement speed instead of 30 and do not receive any special damage bonuses (beyond standard Ranged Cavalry), but otherwise have the same stats as the standard units they replace. They have the ability to gain resources when they damage an enemy resource building at the rate of 1/3 resources per point of damage dealt. This ability only works for Food, Timber, and Metal; buildings that gather Knowledge, Wealth, or Oil are excluded.
Lakota Unique Ranged Cavalry, Gunpowder Age - fast gunpowder-armed raiders able to fire even while moving. Receive plunder each time they damage an enemy building used for gathering (e.g., Granary, Farm).
In the default Conquer the World campaign, eliminating the Lakota and then subsequently playing their nation card in another battle will result in the player starting with no Farms but still being allowed to build them.
If an enemy city is captured that has Farms, those Farms will be destroyed upon capture.