As I understand, you want to make sure the same client is always directed to the same site for recurring request. This is required for session consistency on application level i.e. to maintain a shopping basket because your sites do not synchronize this information in realtime.
If for some reason (i.e. client changes a new DNS resolver in a different region) an A record is provided which points to the other site, you may want to direct the client to the proper site.
This can be done by creating site specific hostnames basket1.domain.bit and basket2.domain.bit along to www.domain.bit.
If the client was initially handled by site 1 the load balancer or application server sets a site specific cookie. With each new request the client will send this cookie, which indicates what site actually has his shopping basket.
Now the LTM can redirect the client to basket1.domain.bit or basket2.domain.bit, if it gets a request with a cookie belonging to the alternative site.