Upgrade Snow Leopard Server to Lion Server. What problems should I expect to arise?
Well, I would advice clearly against doing this for a live system at the moment. Don't fix it if it isn't broken.

Lion Server has a completely revamped UI, it takes quite a bit of time to reconnect all the bits and pieces. It does a lot under the hood which used to be exposed in Server Admin.
DNS / DHCP / other low level services are still available, but not exposed in the default UI anymore.

Set aside a separate machine, learn to find your way in the new UI, and then you may choose to upgrade your live system or not.