Does your program work now? What I find strange is that these lines

            $LC[$i] = $f[$i]/$den;
             $den = 1;
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are within the "$j" loop which looks wrong to me. I would write your code like this (ignoring some of the stylistic advice given so far):

use strict;
use warnings;

sub lagrange {
    my $x = shift;
    my $f = shift;
    my @LC;
    my $n = @$x;
    for (my $i=0; $i < $n; $i++) {
        my $den = 1;
        for (my $j=0; $j < $n; $j++) {
            next if $j == $i;
            $den *= $x->[$i] - $x->[$j];
        }
        $LC[$i] = $f->[$i]/$den;
    }
    return \@LC;
}

sub lageval {
    my $x = shift;
    my $LC = shift;
    my $x0 = shift;
    my $n = @$x;

    my $sum = 0;
    for (my $i=0; $i<$n;$i++) {
        my $mult = $LC->[$i];
        for (my $j = 0; $j<$n; $j++) {
            next if $j == $i;
            $mult *= $x0 - $x->[$j];
        }
        $sum += $mult;
    }
    return $sum;
}

my @x = map { $_ - 2 } 0..4;
my @f = map {$_**2} @x;
my $LC = lagrange \@x, \@f;
my $x0 = 0.5;
my $y = lageval \@x, $LC, $x0;
print "$x0 $y\n";
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