Japanese nicknames
My name is Alexander, and I've been treating Alex as my full given name. I dislike my name in Japanese as it is hard to pronounce, so I would like some help on that, too. My middle name is Lucas, my handle is lualdu, and my old nickname is Lu. Which leads me to the idea of ルウ. Just wondering if that seems too feminine. On top of that, I have no idea how to introduce myself with a nickname. E.g. "My name is Alex, but you can call me ___"

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I'm in the same predicament - my name is Meredith, and there's no "dith" sound at all in Japanese, so I go by メリ (meri) which is fairly similar to my English nickname Merey. I've even gone so far as to pick out kanji for メリ, but that's more for personal use, I don't write メリ with them.

As far as your nickname goes, it doesn't sound too feminine, and you'll often find that Japanese names can be more unisex. I would suggest spelling it ルー, which is how words with long vowel sounds are normally spelled in katakana.

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I don't think ルウ would sound feminine. This kind of sound in a name isn't that common in Japanese, so I suppose it could be quite neutral. As far as how you would introduce yourself, you could say:

私の名前はアレックスです。でも、ルウと呼んでも大丈夫です。
（わたしのなまえはアレックスです。でも、ルウとよんでもだいじょうぶです。）
Literally: My name is Alex, but it's ok if you call me Lu.

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introduce yourself as Lex = レクス