I think it's a little boring and it reminds me of the late 80s and early 90s. It is a classic but classics can sound dated too (e.g.
Amanda,
Stephanie,
Jessica). I wouldn't say it is timeless.
Elizabeth always sounds classic whereas
Amanda, while being a classic, sounds dated and I think
Julia is more like
Amanda than
Elizabeth. It still sounds fresh now but I think it may remind people of the 90s in a few years.
If you like it, use it. It's too common for my taste but it's a nice name. I much prefer
Julie (dated but will make a comeback, I think) and
Juliet.