If you end up needing their email address because you can't send a message on LinkedIn, there's a slew of ways to find someone's email. They might list it on their Twitter, Github, or blog. Companies out there will help you guess it (Clearbit, Hunter, VoilaNorbert, etc.). And if all else fails, googling your best guesses as to what their email is (including their gmail) will often yield a match in some random mailing list, press release, or what have you.