The lookup constraint may be difficult to achieve if the source and destination lists are in different farms or maybe even web applications. Out of the box I am not aware of a tool or command that maintains the lookup if the lookup is not in the list itself (or part of a larger export of a site/site collection/content database).
My first suggestion doesn't satisfy your version to version requirement either, however it's worth pointing out that for SharePoint 2010 (foundation or Server), the Export-SPWeb cmdlet can backup sites, lists, and libraries. To import, you use Import-SPWeb. It might be worth trying if you are dealing with SP2010 only.
Typically the commands would look something like this:
Export-SPWeb -Identity http://sourcewebapp/managedpath/sitecollection -path C:\Backups\listbackup.bak -ItemURL "site/list" -IncludeUserSecurity -IncludeVersions All
Import-SPWeb -Identity http://destinationwebapp/managedpath/newsitecollection -Path C:\Backups\listbackup.bak
In Export-SPWeb you see that the Identity parameter is the source site collection, and with Import-SPWeb it's the destination site collection. You specify the site or list by passing the path to these components with the -ItemURL parameter (I mention this because Microsoft's documentation is slightly confusing).
You'll also notice that Import-SPWeb specifies only the site collection to import into. It will place the exported data into the same location in the new site collection, which means if you have a list that's several levels down from the root site collection, it will restore several levels down in the destination which may not be what you want.
The SharePoint 2007 (WSS 3.0 and MOSS 2007) equivalent for Export-SPWeb and Import-SPWeb were the export and import stsadm operations, however they could only export the site (SPWeb) level.
For commercial tools generally the support for maintaining or mapping the minutia of content is fully supported though these tools may be overkill (read: pricey) for your needs if your list is small, if you don't intend on repeating the migration, or if you don't plan to use these tools for other migrations. I have used and/or know of the following tools:
- Metalogix Migration Manager for SharePoint (disclosure: my company has a partnership with Metalogix). I've used this on large-scale migration projects for upgrades (SPS2003 to MOSS 2007, MOSS 2007 to SP2010) and migrations within and between farms. I have clients that use it for smaller day-to-day moves by their SharePoint Administrators.
- AvePoint DocAve (disclosuse: my company has a non-financial partnership with AvePoint). I have used this product to migrate content between farms. I have less experience with it than I do with Migration Manager and it has worked well in the migrations where we have used it.
- Davinci Migrator (by Axceler) is a product I have never used but hear it works well. Axceler makes the popular SharePoint tool ControlPoint (disclosure: my company does not have a partnership with Axceler and we do have several clients who use their products).
- Migration Manager for SharePoint (Quest) - never used it, but Quest is more or less the de-facto product for AD migrations and I've heard their SharePoint products are on par with the others on my list (disclosure: my company does not have a partnership with Quest).