Hi, I am looking to identify and find a free font from very first edition of Japanese to English dictionary by J.C. Hepburn.

It think it's some variant of Baskerville, but can't find anything quite like this one. Maybe someone will. Here's a better version (book scan in Library of Congress).

Thanks to MissNobody’s bigger sample, I would say it’s some version of Scotch Modern. Century Expanded is similar, but the dictionary predates it. A very popular style to this day, there are countless modern digital offerings, at any price range, that could be considered more or less a match (as a start, you can peruse the "Related typefaces" list in the aforelinked page). Similar free typefaces may include the less contrasted Century Schoolbook, most probably already on your computer, and Old Standard.

If you need to recreate the original look and feel, there are some options as well, for example: Old Times American, Oldkirk, and Century Modern (free for personal use).