Learjet 35 pilot reported an engine throttle lever became sluggish during descent resulting in a large split between engine indications. Flight crew shut down engine and continued to safe landing.

Narrative

On Day 0; at approximately XA30; our aircraft departed ZZZ1 for ZZZ with two passengers on board. Throttle operation during cruise flight was normal. During descent into ZZZ; the number two engine throttle lever response became sluggish; and a significant split was noted between the number one and number two engine indications.Delay vectors were requested from ZZZ Approach to allow troubleshooting. I was the pilot flying (PF) and called for the Abnormal Engine Operation checklist; which was executed by the pilot monitoring (PM) while I handled communications. The checklist produced did not resolve the problem; N1 remained approximately 95% with the throttle lever in the idle position. Due to the inability to descend or reduce airspeed; and with the airport in close proximity; the Engine Shutdown in Flight checklist was initiated. Weather at ZZZ was VFR with no clouds in the vicinity and light winds from the south.Upon placing the number two engine thrust lever in cutoff; the engine continued to operate. Because throttle cutoff did not accomplish engine shutdown; the number two engine fire T handle was pulled; and the engine was secured. ATC was advised with four souls on board and 2;500 lbs of fuel remaining.We landed uneventfully on ZZZ runway XXL and taxied to the FBO without further incident. The fire department met the aircraft upon arrival. Maintenance was notified; and the aircraft was removed from service for inspection.