Lapua brass can be had, they use "7.62x53" designation. As far as I know, that is just the Finnish designation to differentiate their use of .309 bullets. Seeing as how one should size the neck at loading anyways, s/b no problem for your intents. The brass is spoken of to last 10+ loadings with proper care. I know for certain the brass is in stock at Bruno Shooters Supply, I also believe they sell partial boxes.
Can't help you with dies but they should be around. Mine are redding or RCBS, can't remember. You may find dies under the x53 designation, not sure what the ramifications would be for loading.