if a car dealer makes a promise to sell to someone if i don't hear from them in 48 hours, but sell the car to another instead, can they sue?

Depends but likely no. Verbal promises can become enforceable if consideration is given.
If so there is a very high chance they can sue. So basically did the person give the car dealer anything in exchange for this promise? Money is one but it can include other things such as sacrificing a legal right, or doing something that you are not required to do by the law.

They are liable and I can sue. There is the presumption that the dealer and I have a business or commercial relationship and therefore the intention of any agreement we make is legally binding. using the case Bryne v Van Tienhoven (1879-1880) LR 5 CPD 344 if someone promises you something within a reasonable time frame, they are contractually bound to do so. Also, the only way I could not sue is if they had contacted me within that timeframe revoking the offer either by themselves or via a reliable third party.

Car dealers lie. It's expected.

Verbal promise, no deposit then they have no reason/proof to sue

No they cannot.

Yes they can sue, but only for the damages that they suffered (metal anguish isn't damage in this kind of case)

What damage did the customer suffer? How many dollars are they out of pocket?

A car dealer is not obligated to hold onto a car indefinitely based on a verbal promise. If you wanted to buy the car, then you needed to secure your claim to it with a down payment or signing some kind of contract.

Otherwise the seller has no reason to believe that you are a serious buyer, and he has every right to sell to the next person who comes in ready to buy it.

No written promise, no can sue for breached of promise (contract), in my days that was called 'low balling'. The dealer and I agreed to a price and when I showed up at the dealership they claimed we agreed at a different price.

You must be young.
Don't ever believe a car dealer, a politician or a contractor until they have come through with actually having done something.

You have no contract if no money has been exchanged.
And no, you cannot sue.