You're trying to do that by manipulating $., but that won't read more lines. Since you want to keep lines from before the match, you'll need to buffer them. Here's one way,

my $n = 10;  # , say
my @lines;
{
    local $_;
    while (<LOG>) {
        push @lines, $_;
        if (/c9391b56-b174-441b-921c-7d63/) {
#            push @lines, (<LOG>)[0..$n-1] and last;
# better,
            while (<LOG>) {
                push @lines, $_;
                last if @lines > 2*$n;
            }
            last;
        }
        else {
            shift @lines while @lines > $n;
        }
    }
}
[download]

Update: improved the code to not read the rest of the file after a match is found.