Font embedding is an essential feature of PDF, any PDF reader that doesn't support embedded fonts is seriously broken. So yes, you can assume that all ebook readers will display the embedded fonts. Even all ligatures and kerning created by LaTeX will be displayed, as they are "hard-coded" in the PDF (the case is different with ePub, where it is the reading software that must apply these typographic features, and often does not).
Perhaps you want to create a black-and-white ereader version, given that most ebook readers have black-and-white screens (not every ebook reader is an iPad, you know).
As for the font, Lucida is not free, but if you bought a
license you can embed it in PDFs, that shouldn't be a concern. If you don't have a license, maybe the kpfonts package suits your needs.