And this array formula in F2 will get you your Driver (can't believe there's nothing simper, though!):

=INDEX('Race Data'!$I$2:$I$97,CHOOSE(1+(MIN(IF('Race Data'!$E$2:$E$97=Record!$C2,'Race Data'!$N$2:$N$97))<MIN(IF('Race Data'!$E$2:$E$97=Record!$C2,'Race Data'!$O$2:$O$97))),MATCH(MIN(IF('Race Data'!$E$2:$E$97=Record!$C2,'Race Data'!$O$2:$O$97)),'Race Data'!$O$2:$O$97,0),MATCH(MIN(IF('Race Data'!$E$2:$E$97=Record!$C2,'Race Data'!$N$2:$N$97)),'Race Data'!$N$2:$N$97,0)))

Change this part at the start: 'Race Data'!$I$2:$I$97 to 'Race Data'!$C$2:$C$97 and keep everything else the same for the Year.

Notice that there are a few #N/As in there due to Indianapolis Motor Speedway having blanks in the Race time column.

Regards