No. There is no such implication. When we hear or read 'He lost his car.', it is impossible to know what happened next in the story. Maybe he got his car back or maybe he didn't. We would need more context and more information to know whether or not he found it again. [By contrast, when we say the simple statement 'He's lost his car.' - the contraction of 'He has lost his car.' - we're telling you about the current situation. This means that his car is still missing.]

No. It is a simple statement of a situation at a certain time.

If you wanted to convey information about the chance of getting it back you would have to say things like He lost his car permanently. He lost his car for good. He’s temporarily lost his car. He’s briefly carless.

usually it does not.