The following code makes the call successfully.
Changed URI to http (as hossman noticed) and the construct of the onAction header.

#use SOAP::Lite +trace; 
use SOAP::Lite;
my $s = SOAP::Lite
 -> uri('http://my.ephit.com/WebServices/Website')
 -> proxy('http://my-test.ephit.com/webservices/website.asmx')
 -> on_action(sub{sprintf 'http://my.ephit.com/WebServices/Website/%s'
+, $_[1] });

my $Req = SOAP::Data->new(name => 'Req', value => "ASTHMA", type =>'xs
+i:string');
my $Gender = SOAP::Data->new(name => 'Gender', value => "MALE", type =
+> 'xsi:string');
my $Age = SOAP::Data->new(name => 'Age', value => "38", type => 'xsi:i
+nt');
$result = $s->GetConditionsText($Req, $Gender, $Age)->result;

use Data::Dumper;
print Dumper($result);
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