Hi - unfortunately if you are using an internet-facing application there is no way you can guarantee that an LDNS will stay the same during the lifetime of a user session. GTM persistence or static persist will only get you approx 70-80% (in my experience) of HTTP requests hitting the same site :-(, however this is better than 50/50 - you only need to deal with 20-30% of sessions at the wrong site.
If using some kind of inter-site session store (like memcached) is not an option and the session really need to be server persistent, then you'll need to create access from the LTMs of one site, to the servers of the other, either using backend WAN links, or t'internet, either with or without a WOM product.
Once you have the inter-site access setup, you can use priority-group activation to include the servers of one site in the LTM pools of the other site (and vice-versa). There are other ways to deal with this (like site-specific HHTP redirection), however the latter option I describe has worked well for us.