The OP is asking for a way to query between DBs and so I understand the linked server responses. However, if you're here because you simply want to open an SQLite db with MSSMS, it's a lot easier than that.
Call me lazy, but all of these answers are kind of laborious and/or require things you may not want to do, have access to do in every case, or are just the wrong thing to do if all you are looking for is something better than DB Browser For SQLite such as MSSMS.
Just use this: SQLServerCompactSQLiteToolboxforSSMS
Open the Compact Toolbox
Add a connection
Browse to the file
