it can be done with caldav. but locating the endpoint is as I understand it a search in the OSX ~Library. there are a number of threads in the apple communities about locating the endpoint. But not being an OSX user, I can not comment of how simple the procedures discussed are. They sound simple.

Thanks but I am not that familiar with OSX either

have you got it set up on the iphone?

Harvard university offer some advise to ical that readily translates to Lightning. See http://computing.physics.harvard.edu/icloud

They suggest the following

1. Get your calendar set up and up to date in iCloud first. This is key.
2. Open icloud.com in a web browser and go to your calendars.
3. Click on the circular 'wireless' icon to the right of the name of the calendar you want to use.
4. The calendar you want to use must be shared. If it's not, you'll be presented with the option there.
5. Once the calendar is shared, note the name of the server right after webcal:// (example: p02-www.icloud.com)
6. Open your CalDAV client.

My instructions are to add a new calender in Lightning

Fronm Harvard again For server address you need to slightly modify that server name you jotted down in step 3 If the server was p02-www.icloud.com, you would replace www with caldav and enter p02-caldav.icloud.com