I had a Mobile Me account. I didn't upgrade to Lion (from Snow Leopard) but had a message saying that I would still be able to use my email.
My Mail has now stopped receiving from the .me account but still sends ok.
Should I have changed some settings?
Yes. To continue accessing what was your Mobile Me account on Snow Leopard, you need to delete the MobileMe account from Mail and re-create it as an IMAP account. You will not lose any of your mail when you do this.
You may need to hold down option when creating the account, to prevent Snow Leopard's mail from recognizing the .me or .mac address and forcing it to be a MobileMe account. (Mail asks for your email address first, and then asks what kind of account to create. It normally won't ask for account type if it recognizes the address as MobileMe or GMail. Snow Leopard's Mail doesn't know yet that MobileMe is no more, hence the need for holding down the option key at the right time.)