L1, L2, L3 activities

Answer:
L1, L2, L3...are typical for Incident Management process. How many levels i.e. where does certain level belong in ITSM of the company depends on various factors. Here are few examples:
- processes/functions in place
- complexity of IT services supported
- 3rd parties in place (or not in place)
- capability of ITSM employees
- geography of the organization
- etc.

So, according to the organizational setup, so will be L1, L2, etc. job description (including responsibilities) made. For example, Service Desk can have L1 responsibility, L2 could be expert for certain technology and L3 could be development department.
Other processes - usually organizations don't need many levels in e.g. Knowledge Management.