This was addressed before and you might get a better answer by searching the support forums. But, as far as I remember, there isn't any database ID (TMDb, IMDb) in the file. It's basically not built to be imported anywhere else.

I understand what you’re saying. Looking at the files themselves, each item does have a unique “Letterboxd URI”. Following one of these links to a film’s Letterboxd page and highlighting the “Details” tab reveals raw links to both TMDB & IMDB in every case. Unfortunately that’s the limit of my technical knowledge, so I don’t know if this would require a tweaked API (or some other fancy method of programming I know nothing about!) but to me it looks like it could be done with the right expertise?

Technically yeah. But a better and easier way would be for Letterboxd to include the IDs in their export.

Take some time, grab some coffee. It is possible with TraktRater & LibreOffice Calc.