1. Lunch is on me.

2. I'll buy you lunch.
3. I'll take you out to lunch.
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Are they all the same in meaning? Is 'lunch' in #3 used as a verb?

4. Long time no see.
5. It's been a long time.
6. I haven't seen you in ages.
7. It's been so long.
8. I haven't seen you for a long time.
9. It's been a long time since I saw you last.
10. I haven't seen you for a while.
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Are they all the same in meaning? Do you have some more similar expressions?

Yes, 1-3 all mean the same thing. In 3, "lunch" is used as the object of the preposition "of" -- an adverbial prepositional phrase modifying the phrasal verb "take out."

And yes, 4-10 all mean approximately the same thing. There are a couple of even more casual expressions I can think of!

Long time, no see!
It's been ages!

In 3, "lunch" is used as the object of the preposition "to" -- an adverbial prepositional phrase modifying the phrasal verb "take out."

("to" not "of"!)

1. "Lunch is on me": This phrase means that the speaker will pay for the meal. The expression "on me" means that the speaker takes responsibility for covering the cost.

2. "I'll buy you lunch": This phrase also means the speaker will pay for the meal. However, it explicitly mentions that the speaker will personally purchase the meal for the listener.

3. "I'll take you out to lunch": This phrase means the speaker will treat the listener to a meal at a restaurant or eatery. The verb "take" implies that the speaker will accompany the listener to the location.

In all three expressions, "lunch" refers to the midday meal and is used as a noun.

Regarding the second set of expressions:

4. "Long time no see": This phrase is a colloquial way of greeting someone you haven't seen in a while.

5. "It's been a long time": This expression indicates that a considerable amount of time has passed since the speaker last saw the person they are addressing.

6. "I haven't seen you in ages": This expression emphasizes that a significant period has gone by since the last meeting.

7. "It's been so long": Similar to the previous expressions, this phrase indicates a long interval since the speaker and the person being addressed last met.

8. "I haven't seen you for a long time": This sentence conveys that a substantial duration has elapsed since the speaker and the listener last saw each other.

9. "It's been a long time since I saw you last": This expression focuses on the speaker's perspective and emphasizes a long period without seeing the person being addressed.

10. "I haven't seen you for a while": This phrase communicates that there has been a noticeable gap in time since the last encounter.

While these expressions share the general meaning of expressing that it has been a considerable duration since the previous meeting, they may slightly differ in emphasis or formality.