Lawful-intercept is in general implemented at the server equipment of telecom operator, not in the phones. In general, intelligence services don't access phones, if the interception can be done at the operator, because this could alert the subject or expose their techniques.
According to a friend, who is working for an telecom company in Europe, Lawful-intercept is done at a server rack provided by and managed by a law enforcement agency, all traffic of this telecom company is copied to this server rack. The server rack also has a second direct connection to the law enforcement agency. Employees of the telecom company don't know which phone numbers are targeted or which traffic is intercepted.