AN EMB-145 EXPERIENCED A LIGHTNING STRIKE AND SUBSEQUENTLY THE #1 ITT TEMP WENT INTO THE RED. THEY DECLARED AN EMERGENCY AND LANDED AT DEST.

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FLT SEGMENT WAS BTWN ZZZ1 AND ZZZ. ATC HAD CLRED US DIRECT TO ZZZZZ INTXN. THIS ROUTING APPEARED ACCEPTABLE ON THE WX RADAR DISPLAY. AS WE WERE DSNDING THROUGH FL190 WE EXPERIENCED A POSSIBLE LIGHTNING STRIKE. AFTER CHKING ACFT SYS; WE OBSERVED THE ITT PARAMETER ON ENG #1 WAS RISING AND HAD GONE ABOVE THE GREEN RANGE INTO THE AMBER. WITH THE THRUST LEVER IN FLT IDLE THE ITT ROSE INTO THE RED RANGE AND FLUCTUATED FROM RED TO AMBER. WHILE THE FO WAS RUNNING THE ENG ITT OVERTEMP ABNORMAL PROC; ALL OTHER ENG PARAMETERS DISPLAYED NORMAL IN THE GREEN. ENG #1 SEEMED TO BE RUNNING NORMALLY. THE ABNORMAL PROC DIRECTED US TO APPLY THE ENG SEVERE DAMAGE SHUTDOWN PROC. WE DECLARED AN EMER WITH ATC; REQUESTING CFR EQUIP TO BE WAITING. THE FLT ATTENDANT WAS NOTIFIED AND BRIEFED. A SINGLE ENG APCH AND LNDG AT ZZZ WAS COMPLETED UNEVENTFULLY. CFR INSPECTED ENG #1 AND ACFT EXTERIOR THEN ESCORTED US TO THE GATE. ALL PAX DEPLANED VIA JETBRIDGE. POSTFLT INSPECTION REVEALED LIGHTNING HAD ENTERED AT NOSE CONE AND EXITED AT R SIDE WINGTIP AND AILERON TIP; ALSO AT L SIDE HORIZ STABILIZER TIP. DISPATCH AND MAINT CTL WERE NOTIFIED AND MAINT LOGBOOK ENTRY WAS COMPLETED.