If you know anything about military people (especially those involved in TS/SCI-cleared projects), they rarely are found on any social media platforms.
Plus, L.T is much older than most of us. It's no surprise he doesn't have social media presence anyhow
Wouldn't you like to remain as low-key as possible if you had highly disruptive tech?
I do remember seeing something on the news 3 years ago about his EV car being stolen. That was a month or so ago and people did find that story on the news about LT. Did not dig any deeper than that.