Most of the time we’d put that person (team lead, manager, etc) on a higher level of the escalation policy. Having an escalation policy like this gives the local team a few chances to address the incident before notifying management.
Layer 1: Team Primary On-Call
Layer 2: Team Secondary On-Call
Layer 3: Team Lead
Layer 4: Manager
Layer 5: Sr Manager/Director
Layer 6: Executive
There isn’t a way to notify someone outside of this without some external script/automation actively watching the incident and taking action.