• open file 1 and 2
• read one line from each and build a $hash{line1}=line2
• once done open file 3
• output lines from $hash{line3}

update

in case 1 and 2 are very large and 3 is not, then do it the other way round:

• read file 3 into a %seen hash
• iterate again simultanously over 1 and 2
• output lines seen in 3

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11111080
use warnings;

my @file1 = split /^/, <<END;
aa-aa1-aa
aa-aa2-aa
aa-aa2-ab
aa-aa3-bc
END

my @file2 = split /^/, <<END;
V1111:something
V1111:something
V2222:something
V1111:something
END

my @file3 = split /^/, <<END;
aa-aa1-aa
aa-aa2-ab
END

my %one2two;
@one2two{@file1} = @file2;

print $one2two{$_} // '' for @file3;
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Are the records in File1 and File3 unique or are there multiple lines with the same value like File2 ?

Files 1 and 3 only have unique values.

These files are not very large, likely no more than about 200 lines.