Access loadbalanced IP from internal VLAN

So by removing any SNAT, it looks like the return traffic from your servers isn't going back through the BIG-IP for this 192.168.1.0/24 vlan since they are in the same subnet.

One way to fix this is to apply an iRule to your 1.1.1.1 virtual server that will SNAT only if the request is from your internal vlan:

when CLIENT_ACCEPTED {
   if { [IP::addr [IP::client_addr] equals 192.168.1.0/24] }{
      snat automap
   }
}