I haven't played any of Dawnguard yet, but by my understanding from consulting the uesp by receiving Lord Harkon's gift you become cured of lycanthropy, and vice versa during the ritual of The Circle while being a vampire.
So my question is if I receive Lord Harkon's gift after the ritual of The Circle, or if I participate in the ritual after receiving Lord Harkon's gift, would the questlines on either end get messed up?

It would probably be best if you finish the companions storyline before you do any dawnguard stuff if u have the intention of becoming a VL just so you dont break anything.

Can anyone confirm this?

Anyone?

I don't believe it causes problems. Keep multiple saves though or finish companions first.

I've completed the companions line as a vampire lord with no problems. I made a new toon wanting to play dawnguard fresh and I started dawnguard quest line before starting companions. I felt that I was missing out part of the game without doing companions so I went back.

You will lose vampire lord to lycanthropy HOWEVER you can change back to vampire lord immediately without breaking anything (or at least I didn't). Right after I got turned into a werewolf, passed out and was at the Silver Hand camp, I fast traveled back to Castle Volkihar and had Harkon turned me. If you talk to the vampires there, they will give you flak but they won't attack you. If you talk to the companions after losing lycanthropy, they don't say anything at all. It's unlimited to the amount of times you can turn into vampire lord but for lycanthropy, it is said Aela will only turn you one other time.

it causes no issues, as you are not required to be or remain either a vampire or werewolf for any quest of either questline, regardless of the fact that you will be at one or 2 quests be offered or forced to be changed.
you can switch from vampire to werewolf, or vice versa, by speaking to aela or Serana (for serana the option only apears at the end of the dawguard questline) when you are either forced to be a werewolf during companion questline or when you get turned by harkon or serana during the dawnguard questlines.