To install a live site on Local, I recommend you use All-in-One WP Migration (link below).
Through the plugin is an easy process, but you can do it mannually too: Just download wp-content folder, export your database, rename it to local.sql, zip it all together and drag into Local’s interface (it will import your website, just like a Local export).
As for All-in-One WP Migration plugin:
- Install All-in-One WP Migration on your live website
- Create a backup and download it on your computer
- Now create a fresh website installation on Local
- Install All-in-One WP Migration on your new fresh website at Local
- Go to the plugin menu at “Import” and select the file downloaded in step 2
- Follow instructions given by the plugin.
You should have your website correctly installed in Local with that process 
If you need any further help, drop it here!