Tesco is a two page login.
When you get to the 2nd page, from the Lastpass icon select Sites and Save all entered data. The way this seems to work is it creates a new lastpass entry for that site but I think it's speceific to the URL for the 2nd page - to identify it I rename the 2nd site to Tesco Page 2 or similar.
A bit clunky but it seems to work. I left the security number fields blank myself before selecting save all data, but if you want these input automatically you will need to Edit the site fields & input the numbers manually (It will of course save 2 of the digits automatically you enter these before selecting save all data).
Note: If Tesco change their login process, such that the URL for the 2nd page also changes I think this will stop working and you would need to redo.
FYI: Lastpass help is a bit vague about the above situation and points you to the Save all Entered data option, but this didn't work for me when I tried it on the 1st page, it didn't save any more than before.
If anyone else has further info, please advise.