You do NOT need to download SQLite3 executables or libraries.
GUI front ends AND ODBC drivers for SQLite3 have particular versions of SQLite3 statically linked.Werner's driver to be useful over the years since he began publishing it. I do not know what 'the correct ODBC drivers' are for SQLite, but I can attest that I have found Mr.
If that is the case, you can either find and stop or kill that process, or rename the DLL to something like 'delete_me_soon' and retry your installation. Perhaps you are already running some process that has loaded that DLL, causing it to not be overwritable. This leads me to think you have some unique, local problem. I had no trouble whatsoever running Christian Werner's sqliteodbc_w64.exe program a few minutes ago, and it created the said directory and left a bunch of files there, including the same sqlite3odbc.dll which, apparently, could not be written during your installation attempt. (If that pretense is false, you have successfully dodged my question and avoided the likely useful implications of a direct answer to it.)
I will pretend that your 'I' refers to the sqliteodbc_w64.exe process as you ran it and granted its requested privilege elevation, and that it could then either create its installation directory or alter its content.