Oh dear!
I think you have done the right thing with your DS - lying is something that all children do as they think it's the easy way out of a situation (even when it's patently obvious that they are lying they will still use this as a strategy of first resort!), and it's important that we teach our children the value of honesty and integrity.
I think the problem you are now facing is that X hasn't been dealt with previously. Does he behave like this generally/with other children? Or just with your DS? Either way, these are the hallmarks of a bully and it should have been dealt with a lot sooner. Sorry, that doesn't really help you at the moment, I know.
However, I think your DH has probably contributed to it by not dealing with it - and the suggestion to get the other coach involved is, I think, an excellent one, as this will remove any perceived favouritism.
Even though it's hard, I think you will just have to leave things with X's mother - she is, after all, rightly angry/upset that your son has punched hers and if you try and tell her now about her son she isn't going to be in the most receptive frame of mind to listen to you. Could the other coach have a quiet word with her once things have calmed down? She may - once this immediate incident has blown over - be horrified to learn about X and his treatment of your son.
(A bit of an aside really, but also just to point out that your DS is a boy! And sadly boys can resort to the physical as a way of dealing with problems - he is on the brink of puberty and there will be testosterone brewing. Not an excuse, but a bit of a hard reality, I'm afraid. As women we are much less likely to see violence/physical responses as the way to behave).
To help ensure that she sees your son in a more positive light (and hopefully pave the way for a better understanding of the relationship between them) I would also strongly suggest that your son apologises to X and his mother. I know that that will really go against the grain, but you have to separate this specific incident from the rest of the situation in order to help your DS rise above it. He (and you!) will hate it and it will be humiliating, but it will also enforce the message about lying and its seriousness.
After this, I would ensure that your DS and X just don't come into contact any more. If they're playing for different teams, great. If your DH is a coach then he is in a situation to help ensure that they can be kept separate. I would suggest that he talks to any of the other adults involved in the team about the issue to find out if they feel similarly about X - and work together to find a way to deal with it. You never know, they might all have just been hoping they wouldn't have to deal with it.
Sorry for the ramble and hope some of this helps - good luck!
I had an incident with DS1 recently (16, so older than yours) where we caught him stealing money from DH and I, and it's a horrible, horrible feeling to know that your child can behave in such a way, so I really empathise with you.