There is a high level of overlap in beanstalk (bs), basecamp (bc) and lighthouse (lh). Specifically projects (bs, bc, lh), users (bs, bc, lh), and milestones (bc, lh).

It would be fantastic to sync the projects from basecamp to beanstalk and to lighthouse, and do the same for milestones. This would also go for users. So, considering that basecamp would be the center of operations (used by project managers) we could do the following:
1) Create a new project in basecamp. Go to beanstalk and flag that project to be "synced". This would auto-create the repository and auto-create a lighthouse project. It would also auto-create all of the appropriate user accounts.

2) Sync users between Basecamp and beanstalk and lighthouse. If I manage users in lighthouse, it should manage users in beanstalk and lighthouse.

3) Sync Milestones between Basecamp and Lighthouse.

I realize that basecamp has a weaker API that does not allow for many things to be remotely created. However, it does allow most things to be exported. And lighthouse does a great job with their API allowing you to do nearly anything remotely.

The only draw-back is that there is no way to attach events to basecamp so that when a new milestone, project, user is created that beanstalk can know about it and act accordingly.

Another point of integration with Basecamp would be to integrate with Basecamp milestones.

You could say that a commit completes a milestone, or say that a new tag/branch in the SVN completes a milestone.

This milestone would then be counted as completed in Basecamp.