If they're going to continue to use Apple's email address the only thing you have to change in Lycos is the DNS/nameserver entries. The MX and CNAME are only if they will be using yourpeople.com's mail servers. If not whatever you have there can just stay. Just curious, what is there now for MX and CNAME?
I did a quick check on 000. As long as your people don't go over quotas they'll be okay, but 000 will charge if you go over 1.5G disk space or 100G per month transfer. Do some googling on 000webhost review. Mixed reviews, some love some hate, typical internet stuff.
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