Very sorry to hear about your experience. I had something similar and actually meant to hop on here and warn everyone not to pay too early.
I got my VIN assigned on Friday, Sept 23rd and was told 2-5 weeks for delivery. A week later, I was surprised when told it could be delivered the following week.
I still needed to sell my existing car and I wanted to make sure I had payment ready to go. The DA told me I could go ahead and sell my car and she'd send over paperwork along with the payment link 'so my payment wouldn't delay my pickup.'
Well, I had been reading this board carefully for months and after reading the horror stories of Goose Island delays, I did not want to be sending Lucid $150k and then waiting another month for my car. I already thought it was wildly optimistic that she thought Goose Island could turn the car around in a day and it would arrive in Tysons a day after that.
I checked in 4 days later and sure enough, not only had Goose Island not turned it around, they didn't even have it! There was a 'delay in transit' getting there.
Good thing I hadn't sent in payment yet (or sold my car). If I had, I probably would have been as mad as you.
3 days later, the car did make it to Goose Island and she expected it into Tysons the following week. I was going to be up there on Wed and weirdly, at this point, she hedged and said that might be too early. She'd put it down for Wed but also scheduled me for home delivery on Friday if Wed didn't happen.
At this point, I sent in a test payment through Plaid to see how quickly they would get it. Same day it turned out.
The following Tuesday (3 days later), they said the car had passed the PDI and they were told it would get on a truck that day and arrive into Tysons on Wed and if all went well, I could pick it up that day or Thursday.
Originally, I was not going to pay until the the car was actually at Tysons but since the timing was working out for me to be there, I went ahead and paid the balance on Tuesday.
I share all this to say, I think it's a major flaw in Lucid communication that they're actively encouraging people to pay that early. Sure, if everything goes smoothly, you'll get a car in a week after that communication. In my case, it was likely only an extra week after that first week. But I'd argue even that first week is already much worse than a normal car dealership experience where you pay and walk out with your car. So two weeks to me is absurd. Never mind a month or more.
All that said, the major difference between my experience and yours, however, is that I had very good communication throughout. When my DA didn't answer her phone, whoever answered at Tysons was always helpful. They'd ask if they could help and then would look up my order and give me accurate status updates and helped keep the process moving.
I'd say the 1.5 week delay started my ownership experience with a slight negative. If I had paid and had that delay, I would have been very upset. If I had a delay, paid, and no one was telling me what was going on, I'd probably be exactly where you are now.
Since getting the car, I do love it. I'm very much looking forward to the software update. The current version has many glitches but they're not so bad it's affecting my enjoyment. Knowing it's a short window before improvements come certainly helps.
Again, sorry you had such a bad experience. I will add, we were a multi Tesla household. My initial interactions with Tesla for the first few years was overall positive. My recent interactions with them have been less than stellar. Happy to be moving on to the Lucid family.
Sorry for the very long post.