Unfortunately, this is one of the flaws in the way LP arranges domains. The only way I can see to work around this is:

You want -

    http://www.domain1.com/
    http://www.domain2.com/
    http://other.domain1.com/
    http://other.domain2.com/

    and both sub- domains should refer to different sites.

What you need to do is delete the sub-domain over your second domain. Then, create a new sub-domain with its own unique name. Then, use .htaccess, and mod_rewrite all calls for the original sub-domain over the second domain to the new sub-domain. At least, that should work. Get a second opinion before you try it, or e-mail support.

So, let's say you have the domains http://www.domain1.com/ and http://www.domain2.com/ on your account. And, you want to add sub-domains, both called "other" onto both domains. So, you'll now have http://other.domain1.com/ and http://other.domain2.com/ as well. And, you want both sub-domains to access different sites.

So, first, create a new sub-domain from cPanel called http://other2.domain2.com/. Then, delete the sub-domain called http://other.domain2.com/. Now comes the hard part. The following should go into a .htaccess file (but needs to be edited to correspond to your domains!):

I'm not a RewriteEngine expert, so you may want to have someone verify that this code is OK. It should be good though. I took it from here. The examples were for redirecting homepages due to search engine issues, but I modified to fit your need.

That doesn't work! Just tried it on my account. I have no more ideas on how to get this working. My only suggestion is to use a different, but similar, sub-domain for your second domain.