A lot of the information you are looking for can be found on the
Boulder County wiki page.
Both are dispatched by Boulder County on the standard Boulder County talkgroups. I don't know why Lafayette PD's talkgroup is labeled PD 2/Police 2, they only refer to it as "tac." Most of the agency specific talkgroups are for administration and chitchat, actual operations take place on Boulder County's talkgroups with FTAC 11-16 being the preferred for the flat parts of the county.
Not sure why you have TG 2567 & 2660 marked as Lafayette, those should be part of the Department of Corrections.
Lafayette Police are the Lincoln units.
Lafayette Fire are the 2600 units.
Louisville Police are the 400 units.
Louisville Fire are the 2700 units.