The examples with "lassen wir uns" have a different context.
In the example in the question it is a proposal to the other person (Mike) to do something. If you speak to one person it is "lass uns", or "lasst uns" if you speak to more than one, or "lassen Sie uns" to formally address one or more persons.
The imperative (or Adhortativ) construction with "lassen" always uses the imperative form of "lassen" that addresses the other person(s) not including the speaker. It is implied that the speaker is included. This is different from the other imperative form.
Lass uns gehen (speaker and one other person, informal) = gehen wir
Lasst uns gehen (speaker and more than one other person, informal) = gehen wir
Lassen Sie uns gehen (speaker and one or more other persons, formal) = gehen wir
This form with lassen is only possible as an alternative to the standard imperative form for the first person plural, it cannot be used to replace the standard imperative form for other persons, e.g. 2nd person singular (geh).