As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
LEARJET N26AT WAS ON THE WAY FROM ELP TO LAX AT FL 410, THE CREW WAS EXPERIENCING SEVERE WEATHER AND REQUESTED TO GO TO FL 450. DURING THE CLIMB THEY HIT TURBULENCE AND THE LT ENGINE FLAMED OUT. THEN REQUESTED TO GO DOWN TO FL 250, RELIT THE LT ENGINE, THEN CLIMBED BACK TO FL 410 AND CONTINUED THE FLIGHT WITH NO FURTHER INTERRUPTIONS.