Stamina, health and magicka do not regenerate while you're in sunlight as both a vampire and vampire lord. One of the many minor annoyances about it, IMHO. :/ If you want to stay a vampire and not go get a cure from the mage in Morthal, I would suggest enchanting yourself some fire resistance armor or clothing to walk around in the sunlight with. Alchemy can help with this as well. Just drink some fire resist potions. It should tell you how weak you are to fire in your Magic menu under Effects in a percentage, so drink enough fire resist potions to match that. They do stack, I believe. There are also potions to jump start stamina, health and magicka regen. All of which you can buy or make.
You could also do the whole vampire roleplay thing and only go out at night. Blood Potions will help you feed while traveling across Skyrim and should hold off some ill effects, which you should have access to with the Dawnguard DLC at Volkihar Castle. Feeding, as others have said, helps this a lot as well. I believe you can feed with the Drain Life spell in the Destruction magic menu, and if you transform into a Vampire Lord and thrall them, then feed, or as a finishing move when attacking. I think you can also sneak and there should be an option to feed. Sleeping NPCs are ideal to feed on, too.
Hope this helps somewhat. If you have any other questions, feel free to ask.
I'll answer the best I can.
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