Headcannons:

The ability to turn people into vampires is reduced as the bloodline is diluted. However, Lucy's Dam was near pureblood so Lucy's close enough to the source to be able to turn Natsu. Technically, this makes her Natsu's Dam, but they're not entirely aware of that fact so Lucy has never used the power she would have over him.

Neither Lucy nor Natsu have ever been particularly bothered by the whole 'killing to Feed' thing. They've accepted that they're monsters and that's what they need to do to survive. They've also always been somewhat outcast from society.

Even before being turned, Natsu and Lucy experimented sexually with each other. It wasn't so much an attraction thing as it was a trust thing and not really knowing anyone else. However, they never developed romantic feelings for each other and quickly moved on to picking up people in clubs and things. This continued into being vampires. Although they generally sleep with different people, sometimes they'll both be involved in a threesome. They both think the other is attractive anyway, even if they're just friends.

Over the centuries, Lucy and Natsu don't necessarily spend the entire time together. Sometimes they'll get annoyed at each other or just want different company for a while and won't see each other for a few years. For them, however, it's basically just a blink in time and they always reconnect.

They're pretty good at keeping up with the times. They wear modern clothing and use the latest technologies. They have amassed enough money over the years to be able to do this (they have bank accounts, though they change bank every 50 years or so).

They move around pretty regularly (for them - remember, time frames are quite different). This is partially because they get bored and partially because there'll be a string of murders following them because of their Feeding. They moved countries sometimes too.

Other Fairy Tail members are present in this AU: Wendy is a very young vampire who was also turned at a young age, Natsu and Lucy basically adopt her and are quite protective of her. Gray is a werewolf (werewolves have very extended lifespans but aren't immortal like vampires). They've known him for many years and meet up regularly. 'Dragon Slayers' are all Vampires, though varying purity.