ASL is a layer 3 device and routing and forwarding is done based on logical addressing. Not by name.
ALternative sollutions:
1. If you have additional public ip:s to assign to the external ASL NIC. Do so and change the DNS record for the site. And of course some NAT and filter rules.
2. If you only have 1 static ip to work with.
alt. a) change the port for the new site or old site.
ex. old: 8080, new: 80 and set up the NAT rules
DNAT 8080 ==> old server
DNAT 80 ==> new server
Of course the remote host need to address the old site with the additional port info (
http://oldsite.com:8080)
alt. b) Set up the reverse proxy module for Apache to redirect the remote client to correct webserver based on the dns-name. Ie.
www.oldsite.com ==> old web server,
www.newsite.com ==> new webserver.