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.

Clause Complex With Non-Finite Hypotactic Elaboration

Every night, at exactly 21:53, the Chief Yeoman Warder of the Tower emerges from the Byward Tower	wearing his long red coat and Tudor bonnet	and carrying a candle lantern and the Queen's Keys
a	= b
	1	+ 2

Reasoning:

Consider the finite agnates of the dependent clauses in the following, where they are presented as enclosed within the primary clause:

Every night, at exactly 21:53, the Chief Yeoman Warder of the Tower << who wears his long red coat and Tudor bonnet and carries a candle lantern and the Queen's Keys >> emerges from the Byward Tower.

The finite agnates of the dependent clauses are clearly non-defining relative clauses, which are instances of hypotactic elaboration — not enhancement.

Why The Unmarked Positive Imperative Clause Is Finite

Check	the Mood Tag	will	you
Predicator	Complement	Finite	Subject
Residue		Mood Tag

See Halliday & Matthiessen (2004: 138-40).