Maybe you've heard of that book, Never Eat Alone: And Other Secrets to Success. I very much dislike when people offer it up as great career advice. The book is decent, but it too often gets way oversimplified.
Quiet, thoughtful leaders are finally getting due credit; I'm pretty sure they eat lunch alone at least once a week. I'm so grateful for Susan Cain, the important work she did writing Quiet, and the "Quiet Revolution" she has started. She and others in her cause have taken the idea that you have to be extraverted and on all the time to be successful in business/life, and turned it on its ear.
You can do productive, career-enhancing things by eating lunch alone. Meditate to prime your mind for second half of your day, storyboard, collect your thoughts.
As a solopreneur, I sometimes forget to eat lunch at all. With all these fantastic digital products and tools, I can leverage my time and energies really well. However, it does mean that I'm doing everything by myself, meaning I don't always have time to step away.
Whether you eat with someone or not, re-frame your lunch time as time spent cultivating — whether that be internally or externally. So, eat lunch alone sometimes! It'll all come out in the wash.