Two Different Lexicogrammatical Realisations Of Offers

Let’s	go out	to lunch	—	(it will be/is)	my treat
Subject	Predicator	Adjunct		ellipsis: Subject + Finite	Complement
Mood	Residue				Residue

Reasoning:

Speech Function And Mood:

Viewed 'from above', in terms of speech function, each of these clauses realises an offer

(offering to go eat and offering to pay).

Offers have no congruent grammatical realisation.

Here, the first offer is realised as a clause of imperative mood;

while the second is realised as a clause of indicative: declarative mood.

Cohesion:

The second clause is cohesively tied to the first clause by the ellipsis of its Mood element.

Logico-Semantic Relation & Taxis:

Viewed 'from below', the graphology suggests a structural relation, such that the two clauses form a nexus, related tactically and logico-semantically.  Since both clauses are independent clauses, they are related paratactically.  Since the second clause adds to the first, the logico-semantic relation is expansion: extension.