Putting the photos on a server is not a problem, Lightroom can handle that.
Having the work synced between two computers: that's a problem. The easiest way to get this to work is to have the catalog on an external HD and move the external HD from computer to computer as needed. If that's not possible, then there really aren't good methods that I know of to work on the same catalog file on two different computers. Each method has serious drawbacks.
For example, you could upload the catalog to the server when you are finished and then download the catalog when you arrive at computer #2, and so on, but the drawback is that if you make a mistake somewhere in this process, then you now have caused yourself to lose information and possibly have catalog files that are out of sync. You can't simply access the catalog file on the server, Lightroom won't allow that.
I wish Adobe should develop cloud based application in LR wherein we can dispense with desktop application
What I wished is very much available in present LR
Uplink images in to web collection(I do it with smart preview)
When the user is logged-in with their Adobe ID it is possible to open a web collection in desk top. No need to have LR installed
Now open your collection in web page of LR & do Editing
In continuation of my above post- That way you can work from any computer which does not have even desktop LR application. Whatever changes you make in web LR page will be incorporated in your server as & when it is connected to net. Hope this is what you are looking for
Think that moving the files on a external HD is the answer, however complicated.....:(
Mike has a useful video tutorial at Tip Squirrel which uses drop box. The important point is not to sync the catalog which LR constantly writes to, but to sync just smart previews.