If Sprint Planning One is for teams to clarify backlog items as a group and select which items they take into Sprint Planning Two (SP2), then SP2 is for agreeing design decisions and creating the Sprint Backlog.
The LeSS approach to SP2 would look like this:
Part 1 (Teams working on closely aligned items can undertake this part together)
- Identify common and shared tasks
- Have a 30 minute design session
Part 2 (Single team sessions)
- Focused on sprint planning as a team
- Create Sprint Backlog
Part 3 (Multi-team design workshop, if needed)
- Delve deeper into common and consistent design for the work
- Agree on design approach and common technical tasks.
In my experience teams will want to have major design decisions already made and approved prior to starting the Sprint that they are going to build in. I would therefore say that although in the ideal LeSS world, design should be done as close as possible to coding activities, in practice, it is advisable to hold your design workshops in preceding Sprints as getting these design decisions discussed, agreed and approved by multiple teams often takes weeks of conversations back and forth.
Assuming you have an agreed design as you move into SP2, the rest of your SP2 will be focused on creating the Sprint Backlog.