I'm only level 6 on my current character, and I entered Lost Valkygg. Inside are leveled Draugr, and I had a time fighting them. But none of them compared to the Draugr Deathlord near the end.

He had an Ebony Bow and Ebony Arrows as well as Unrelenting Force and Disarm. It took me several tries, and a lot of thinking but I eventually defeated him (with the help of Janessa). To understand how hard he was (I was on level 6 by the way), one hit by his Ebony Bow+Ebony Arrow was a one-hit-kill for me and my fur armor (even on Novice difficulty) and my Battle Cry power didn't work.

Thing is, I am now level 6 and I have an Ebony Bow. My question is: if I make a new character one day and go back to Lost Valkygg, will that Draugr Deathlord always be there? And will he always carry the Ebony Bow?

Looking at the wiki page, Deathlords spawn there at very low levels. It'll probably have an ebony weapon, but it may not be a bow.

It didn't say anything about Deathlord's when I looked at the wiki.

The Elder Scrolls Wiki does. A quick skim through the Unofficial Elder Scrolls Pages doesn't seem to mention it.

Most people seem to swear by the UESP. I usually use the wiki, but also refer to the UESP when I find the wiki lacking.

Another place to be weary of at low levels is Arcwind Point. I remember my first time finding that place on accident (after watching a dragon that I was fighting from the nearby Autumnwatch Tower get wrecked from something beyond the mountains, turned out to be two snowy sabre cats). I was like level 10 at the time. I was not prepared for the Deathlord that awaited me there.

Those two places will always have the high level deathlords.

If you got a Deathlord at level 6 you will probably face a Death Overlord later on.