Lived realities?

This is very poetic. The only change I would make is to say "dreams" instead of "a dream" in order to match the plural "realities."

Thanks for your response. I actually thought "lived realities" would be redundant as it's obvious that you live a reality. I thought the sentence should've been something like "I have lived many of my dreams". Thanks for confirming that the original is almost correct.

Would it also be correct to say the following?

"Women and men are forced to live a reality in which their lives are less valued simply because of the color of their skin."

Your "non-redundant sentence is fine, but the meaning of
"I have lived many of my dreams" is not the same as "I have lived many realities that were once dreams." It is possible to live in a reality that was originally dreamed up by someone else.

For example:

Martin Luther King dreamed of a world free from racial prejudice and I hope one day to live in that real

I would probably word it differently but you could say it like that.
It is mostly a matter of style.
A shorter version would be ...forced to live as if their lives were..