Use '?' to get a nongreedy match up to the first newline:

$data =~ m/Line3 : (.*?)\n/s;
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You can also use a greedy match with a negated character class:

$data =~ m/Line3 : ([^\n]*)/s;
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My test code follows:

use warnings;
use strict;

my $data = join( '', <DATA> );
print "[$data]\n\n";

$data =~ m/Line3 : (.*?)\n/s or die;
print "match: [$1]\n";

$data =~ m/Line3 : ([^\n]*)/s or die;
print "match: [$1]\n";

__DATA__
Line1 : Dit is de eerste regel
Line2 : Dit is de tweede regel
Line3 : Dit is de derde regel
Line4 : Dit is de vierde regel
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