PHP mail() is severely restricted on Lenyxo Hosting. Although some messages sent using the mail() function may succeed, generally most messages will be rejected by the mail system.
If you want to send mail from your website, the easiest way would be to use an external SMTP service. Using PHPMailer in combination with Gmail is one such option. Additionally, there are also other SMTP providers that will simply forward mail to your Gmail account.
The simplest solution to use PHP mail() would be to upgrade to premium hosting, which has much higher sending limits and has no filters on PHP mail().