Regarding the price: I can't really say definitely for LX market, but suspect it is the similar as what I've been seeing for LC. There is more supply for LXs so probably not as bad.
Here is a rough example for quite a few listings - if the trade in appraisal values is $30k, private sale around $35k and dealer price is $40k-45k. I see a lot of private seller list for 48k-50k, yes ridiculously above dealer prices, not all but a lot.
When checking many appraisal sites, KBB, nada, edmunds, etc. what you see does not support the private sale number the seller wants. When you ask, they will tell you they don't transaction at that price, but the disconnect is that they do and dealer prices do match KBB, nada and edmunds. Some of them will wait months before admitting if they don't get let's say get mid of what dealer price is they will just keep it. So the answer to your question, there are quite a few sellers who want to beat dealer price or they don't want to sell.
When the car is listed in good condition, priced fairly, it will be gone within couple of days if not on the same. But in today's market this is becoming rare.
Condition of the vehicle (fair, clean, excellent etc) vs what is being asked for, is totally a different story. Quality of used cars, not just LX or LCs have dramatically dropped across all used cars.
Just keep in mind appraisal values are ranges, so if it tells you 35k, it actually maybe be 32 to 39, if you find a gem, don't hesitate to add few Ks.
