Diablo 3 Hardcore Character just died during a 10+ second lag spike, will I be able to get him back?

From the manual of Diablo 2

Note: Blizzard Entertainment is in no way responsible for your Hardcore character. If you choose to create and play a Hardcore character, you do so at your own risk. Blizzard is not responsible for the death and loss of your hardcore characters for any reason including Internet lag, bugs, Acts of God, your little sister, or any other reason whatsoever. Consult the End User License Agreement for more details. Blizzard will not, and does not have the capability to restore any deceased Hardcore characters. Don't even ask. La-la-la-la-la, we can't hear you...

Probably carries over to Diablo 3.

Nope. No compensation. This is what hardcore mode is all about. It encourages a much more conservative play style, and much more attention to the performance of your computer.

If you can't take the heat, stay out of the kitchen.