I would suggest you try the html tag <br>, in case your marketing application will recognize it.
I use %0D%0A. This should work as long as the email is HTML formatted.
<a href="https://stackoverflow.com/questions/22765834/mailto:email@mycompany.com?subject=Subscribe&body=Lastame%20%3A%0D%0AFirstname%20%3A"><img alt="Subscribe" class="center" height="50" src="subscribe.png" style="width: 137px; height: 50px; color: #4da6f7; font-size: 20px; display: block;" width="137"></a>
You will likely want to take out the %20 before Firstname, otherwise you will have a space as the first character on the next line.
A note, when I tested this with your code, it worked (along with some extra spacing). Are you using a mail client that doesn’t allow HTML formatting?