Wow! good question! I think the open source BlazeDS is leaning toward the use of Tomcat Application Server. I have it currently bundled with BlazeDS and tweaked for its use. I would imagine that you could use the Trial version of the Adobe LiveCycle (BlazeDS on steriods) with any of the mentioned version.
Our experience is BlazeDS can be difficult to transition from one application server to another, specifically when it comes to single sign on and session replication in a cluster (at least those are the problems we've found so far). Since these are more advanced issues I assume fixes will come along for the various issues, but I'd suggest prototyping BlazeDS on your chosen container using your chosen authntication mechanism early in your development.
If BlazeDS does not work well in a cluster, what's the point to use it? Does it support asynchronous push to Flex or AIR clients as LCDS?
Why not just use plain servlets to handle HTTP requests and return XML?
Http sessions with plain servlet can be easily replicated in a cluster of any JEE Servers.
subject: Does BlazeDS require EJB container or just Servlet container?