To link your LSP.expert account to your Google Calendar, you have to click on 'Connect my Google Calendar' under Settings > Integration.
Google will then ask you which Gmail account you would like to use. After you selected your account, you will be redirected to LSP.expert with this screen:
You can click on 'Edit options' to indicate if you would like to synchronize the jobs for all users (Team version) and if you want to use the start date of the jobs as the start date in Google Calendar.
In your Calendar, the jobs will have the same colors as in LSP.expert:
Blue: In progress