I was at one time in position, where I was looking for new work and so I send my CV to where I think it could be interesting. In companies anything take time and results are not immediate.
In the end I had proposals (and interview) from 5 companies at the same time (spread over two weeks), I aced all of them, all said something to mean "we love, what we had seen and hear, but we have to wait some time before we will offer you the work, as there are more candidates and also our higher-ups have to say yes to that, we will call you soon".
The interwiev is everitime two way event - they evaluate me, I evaluate them. If both part fall in love, then it is perfect and marriage is on the way. If one is not happy or satisfied, it will not work.
So I also want wait, till I get all interviews and then choose, witch I would like most and where they would want me.
It ended that I made my mind for one particular company (while others if rated like 85%-95% of the winner and would like work for any of them) and in reasonable time I called them, how they see it (well, I had friends in every of those companies, so I could call informal) - was told, they would call me anyway the next day, if I would work for them. So the next day I came there in person and signed work contract. At the same day I got 4 more calls from those others companies and I politely decline their offers, and told them I already accepted other proposal that same day.
I am sure, I was not the only person at any of that companies, that they interviewed and which succeed the interview - I just was free to start working next day (which some others was not and so I got advance even if I may be just the same good as those others). Maybe I was like few percent better, than some other candidates too.
The result was, that I turned down 4 positions and so 4 companies probably just called the second in line (which maybe was as good (or even slightly more), just not avaiable just now, or was reaaly good, just a hair split less than me) for the proposal, that ther first rejected (with something like "sorry, we like you, but we have another candidate who matched the skill-set required and is available immediately"), and told them something to the term, that if they are still interested and avaiable, they would like talk with them again about the position.
Not exactly as your situation, but something similar could happened to you too. You met their criteria, just there was someone else, who met them too and was available. Then he retracted and they have to choose between others, who also met the criteria, but was not choosen at first round. Or they just need to take you when you are free and "be in contact until then", as it is possible, that you also get more offers and will choose someone else. Or they just see, that they can get more than one person, and so want you too, if possible and have you as near as possible, so you would not look another way, until your notice is due ...
IMHO it is perfectly possible, that just "something happened" and they found possible way, how to employ you, just they have to make sure, it would work (so they cannot employ you now, until there is budget signed on their table, but they want you to get familiar with the team and if all came the expected way, that you are still thinking about working for them and nobody other).
Or maybe they are about to open another similar position, and think, that you have also skillset for that, but not sure, if you would like that position and the position is not yet perfectly described, so the talk can help see, if they have to go with the all process describing such position and interviewing people for it, or if you just can fit it (maybe with some small changes) and they can get you (as they already wants you in the team).
If you are interested, I recommend to go to that lunch and talk with them more. It is not as formal as interview and can also tell you more about that company, then formal interview, so you can make decision based on more knowledge.
Interpersonal relations are often more important, than some small differencies in skill-sets, or job descriptions or benefits offered. I would go, will be positive, and (reasonably) open, ask a lot of questions and listen to their chatting too. I would not bet my life on the result and would not be sad, if it would not result in job offer, but it is good sign and good chance for you too to know, if you really want work there. Better know, if both sides are on the same note and eventually leave before contract happens, than discover it whan it is late and contract is alredy signed. (That is for BOTH sides.)
Be prepare, that you will be anyway evaluated there, (more for personality, than for skill-set - and maybe it would not be on conscious level) and be prepare to evaluate them as well. This time it is (or should be) more like you are interviewing them, than they re-interviewing you :)