Same issue for me: Edge Chromium (79.0.309.65, official build, 64 bit) italian language.
Please note: I think this issue is related to italian (or, in general, to non-english) release, in fact if you change language setting (in Edge) to english the Lastpass plugin install is done successfully (but if you revert Edge to Italian... nope... the plugin is automatically "deleted").
PS.: A possible work-around is to install (in Edge Chromium) Lastpass plugin from the Google Chrome webstore (you must enable "consensti estensioni da altri archivi" in Edge), it works, also in italian. Please note that in the Chrome webstore current Lastpass release is 4.40.2 (15-January-2020) and in Microsoft Edge Addons is 22.214.171.124 (9-January-2020)
(from Turin, Italy)