INFLT ENG SHUTDOWN AND ALTDEV.

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ACFT IS AN LR-36; OPERATED BY AN FAR-135 CHARTER COMPANY. WE WERE ON COMPANY BUSINESS; OPERATING UNDER FAR-91. 3 COMPANY PERSONNEL (INCLUDING PLTS) AND 3 GUESTS WERE ENRTE; FMY DIRECT YIP; AT FL450/0;077 IMN. THERE WERE CLUSTERS OF TSTMS AROUND 20 NM W OF DQN AND OVER TOLEDO AND E; WITH TOPS TO FL350. APCHING DQN FROM THE S; WE WERE WELL CLR OF THE CELLS; BUT I ASKED ZOB TO KEEP US HIGH AS LONG AS POSSIBLE; DUE TO RPTED LOW LEVEL TURB. ABOUT 50 NM S OF DQN; #2 ENG FUEL COMPUTER AUTOMATIC MODE FAILED. IT WAS CTLABLE IN MANUAL MODE. I OPTED TO DELAY BRINGING THE ENG BACK TO 50-60 PERCENT N1 (TO RESET; PER EMER CHKLIST) UNTIL WE WERE WITHIN THE PROBABLE RELIGHT ENVELOPE AND BETTER ABLE TO AFFORD A DSCNT. (FROM OUR RADAR PICTURE AND VISUAL SIGHTING OF LIGHTNING E AND W OF OUR COURSE; FL350 AND BELOW LOOKED SAFER N OF DQN THAN S OF DQN.) WHILE REDUCING PWR DURING THE DSCNT; ABOUT 75 NM N OF DQN; #2 WOULD NOT RESPOND TO THROTTLE AND RAN TO 100.5 PERCENT N1. AT THAT POINT; I SHUT IT DOWN; DECLARED AN EMER; AND RECEIVED CLRNC DIRECT TO YIP FOR THE ILS RWY 5. HE HAD OBTAINED YIP ATIS. AT FL180; HE CALLED '.54.' I SAID '30.54?' HE SAID 'YEAH.' (IT WAS 29.54.) AS WE DSNDED ABOUT 500 FT BELOW OUR ASSIGNED 2400 FT; YIP TWR CALLED A LOW ALT ALERT. AT THAT POINT; WE HAD GND CONTACT; AND MY FO TOLD YIP TWR THAT WE'D REMAIN VFR. (HE HADN'T CONSULTED ME ABOUT THAT.) I IMMEDIATELY CLBED BACK TO 2400 FT; AS THE VISIBILITY LOOKED TOO MARGINAL FOR DODGING TWRS IN A JET. WE LANDED; WITHOUT FURTHER INCIDENT. THERE WERE SEVERAL THINGS I COULD'VE DONE DIFFERENTLY. (EXAMPLE: DON'T FLY OVER AN AREA OF SUSPECTED SEVERE TURB THAT YOU'D RATHER NOT DSND INTO.) ATC COULD'VE BEEN A LOT MORE FLEXIBLE. (ABOUT 100 NM BEFORE THE ENG SHUT DOWN; WE HAD TO BEG AND PLEAD REPEATEDLY; TO STAY ABOVE THE ROUGH STUFF; INSTEAD OF PLUNGING DOWN EARLY ON THEIR 'STANDARD' DSCNT. WE DID IT THEIR WAY; RATHER THAN DECLARE AN EMER TO STAY HIGH. I DOUBT THAT THEIR TFC INTO DTW WAS THAT BAD; AT XA30 ON A SUNDAY NIGHT). MY FO HAS 3000 LEAR JET HRS BUT PRACTICALLY NO TRAINING OR EXPERIENCE IN LR-30 SERIES. HE IS NOT A LINE PLT. HE FLIES VERY SELDOM. HIS MEANDERINGS THROUGH BOTH NORMAL AND ABNORMAL CHKLISTS WERE VERY SLOW AND INCOMPLETE; AT A TIME WHEN I WAS TOO BUSY TO DO HIS JOB. RECURRENT FO TRAINING WOULD BE 'NICE.'