What li_fat_id actually is
li_fat_id, LinkedIn's First-party Ad Tracking ID, is appended to the landing page URL when someone clicks a LinkedIn ad. On its own that puts it in the same family as fbclid or gclid: a per-click identifier meant to join an ad impression to whatever happens next on the advertiser's site.
Why it needs the Insight Tag to do anything
Here is where it stops behaving like the others. li_fat_id only becomes useful if the destination site has the LinkedIn Insight Tag installed with enhanced, first-party conversion tracking switched on. When that's in place, the Insight Tag reads the value out of the URL and writes it into a first-party cookie on the advertiser's own domain, rather than leaving it to sit in the URL as a one-time read. Without the Insight Tag installed, li_fat_id still shows up on the URL exactly the same way; it just has nothing on the page to read it, and nothing downstream ever uses it.
That stored-cookie behaviour also means li_fat_id can outlive the single page load a value like fbclid is normally read on, persisting for LinkedIn's conversion matching across a visit rather than being consumed once and discarded.
Is it safe to remove?
You, the visitor, lose nothing by stripping it. For an advertiser running LinkedIn campaigns with the Insight Tag active, removing it before the page loads breaks the cookie write and with it LinkedIn's ability to match a later conversion back to the click. One practical limit worth knowing either way: the first-party cookie it produces typically lasts on the order of a week, shorter still under Safari's tracking restrictions on iOS, so li_fat_id's usefulness for attribution has a real expiry even when everything is configured correctly.