Rich people's lives are the most complicated (ones)—and also the most meaningless (ones).
Can I omit both? If not, which one should I keep?
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Yes, you can eliminate both ones. Your sentence would look like this:
Rich people's lives are the most complicated — and also the most meaningless.
This reads fluently and looks better than the original on paper.
To make the sentence read better, you could consider removing the also, as @J.R. commented. Doing this will give:
Rich people's lives are the most complicated — and the most meaningless.