ALTDEV ALT EXCURSION OCCURS AFTER ACR MDT SUFFERS A LIGHTNING STRIKE IN PROX OF TSTM ACTIVITY.

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AT XA14Z FLT DEPARTED ORD FOR MADISON; WI. ON THE TAXI OUT THE CREW WENT THROUGH THE RWY 27L PAD AND MADE A 360 DEG TURN AND USED THE RADAR TO EVALUATE THE WX. THE SKY IN THE DIRECTION OF FLT WAS CLR. ABOUT 5 MINS AFTER DEPARTING RWY 22L; THE CREW ENCOUNTERED A SMALL LINE OF THUNDER CLOUDS. ATC AUTHORIZED AN EASTERLY DEV AROUND THIS WX. ANOTHER MORE SEVERE LINE WAS ON THE OTHER SIDE OF THIS LINE. THE CREW REQUESTED AND RECEIVED CLRNC TO PARALLEL THE BACK SIDE OF THIS LINE. AN ALT OF 13000 FT WAS ASSIGNED. BEFORE CONTACTING ATC ON THE NEW FREQ; THE ACFT RECEIVED A LIGHTNING STRIKE TO THE RADAR DOME AREA. THERE WAS A LOUD BANG; A FLASH; AND A SHARP RAP ON THE RUDDER PEDDLES. A QUICK SURVEY OF THE FLT SYS AND EQUIP INDICATED A LOSS OF THE L AC WILD GENERATOR. THE CAPT'S AND FO'S HDG AND ATTITUDE INSTS WERE LOST. THE FO TRIED TO CONTINUE FLYING USING THE STANDBY GYROSCOPE; BUT THE LOCATION OF THIS INST MADE FLYING FROM THE R SEAT VERY DIFFICULT. THEREFORE; CTL WAS TRANSFERRED TO THE CAPT. IN THE PROCESS OF TRYING TO REGAIN CTL OF THE SIT THE ACFT INADVERTENTLY WENT TO 13570 FT. ZAU WAS NOTIFIED OF THE PROB AND THE FLT RECEIVED PRIORITY HANDLING. THE WX AT THE NEAREST ARPT AND CHICAGO WAS WORSE THAN MADISON; SO THE FLT HEADED THERE. AN UNEVENTFUL ILS LNDG WAS MADE IN MADISON. A POST-FLT INSPECTION OF THE AIRPLANE REVEALED BURNT AND CHARRED PAINT ON THE NOSEWHEEL LNDG GEAR DOORS. AN EXIT HOLE WAS FOUND AT THE TIP OF ONE OF THE PROP BLADES ON THE #1 ENG. THE LAST FOOT OR SO OF THE COMPOSITELY CONSTRUCTED BLADE WAS PUFFED OUT TO A THICKNESS OF ABOUT 2 INCHES. THE VERY TIP WAS BLOWN APART ABOUT 1/2 INCH EXPOSING A CHARRED INTERIOR. NO OTHER SIGNS OF DAMAGE WERE DISCOVERED.