I am going to assume the code was meant to look like so until you fix your code tags.

my @arr_in_1 =("User1","user2","user3"); 
my @arr_in_2 =("user2","user3","User4"); 

my @union_arr; 
foreach my $arr_1(@arr_in_1) 
{ 
   push(@union_arr,$arr_1);
} 

foreach my $arr_1(@arr_in_1) 
{ 
  #print "The value in array 1 is :" .lc $arr_1."\n";
  foreach my $arr_2(@arr_in_2) 
  { 
     #print "the value in array 2 is :". lc $arr_2." \n";
     if (lc $arr_2 ne lc $arr_1) 
     { 
        push(@union_arr,$arr_2); 
     } 
  } 
} 

print "union array @union_arr";
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The main problem is the statement lc $arr_2 ne lc $arr_1 which will always result in truth (in this case). For instance think about what is being compared.

first loop(first element in @arr_in_1) vs inner loop(@arr_in_2):
user1 ne user2 (true)
user1 ne user3 (true)
user1 ne user4 (true)
so obviously this is inserted into the union array.

second loop:
user2 ne user2 (false)
user2 ne user3 (true) Again pushed into the union array
...

Well you get my drift. Your on the right track just have to make a couple modifications.

-enlil