Using LTM for network forwarding

Our data center architecture has a pretty standard model, with an "internal" network and a "DMZ". Our internal network does not have a direct route to the Internet. However, I have LTMs in our DMZ that can access the Internet directly. We have a server in our internal network running Microsoft Office 365 "Hybrid services" that needs to access a number of Microsoft Office 365 public networks, and I am being asked to facilitate this connectivity with our LTM. But given my lack of networking knowledge, I don't quite understand how I might configure the LTM to do this. I get a bit lost when it comes to how the different VS types function.

I was hoping someone might be able to help me understand at a high lievel what we would need to do in our network gear, and on the LTM, to enable this communication?