Just translating Italian with Italian might lose a key reason for these entries, namely, D>E, for people who come across German terms in pieces by German composers and don't otherwise speak German. Everyone who studies music in any language learns the Italian terms early, but many English speakers will have to look up words like this in German (and the equivalent in French).
So I wouldn't support deleting the German altogether, though I wonder whether lebhaft and fröhlich really translate as vivace. On the face of it, they sound actually more like allegro, which is brisk but not as fast. I would be curious what the musicians say, whether they would really read lebhaft as very fast, vivace (say 150-160) or just as fairly fast, allegro (say 130-140). I don't know, that may differ enough in period performance that you can't absolutely generalize -- I have a vague recollection that in earlier music the terms were used somewhat differently, so that a baroque vivace was more like the literal Italian etymology, just a lively pace, not lickety-split. (IIRC, which I may not.) But I'm thinking mainly just from the point of view of general music education at a less specialized level, like the average amateur musician, or child or teenager taking music lessons.