I have successfully imported the complete vault from Lastpass several times. The process that seems to work best for me is to do the following:
Export Vault from Lastpass
Select all text and save as plaintext file with ".csv" extension
Open file in Excel (or some other spreadsheet program, Google Docs, LibreOffice, etc.)
Save file as CSV file from inside the spreadsheet software
Import resulting file into Enpass using the Lastpass import type
Every time I have done this I got a complete import of all the data.