Often times your website host provides you with hosted e-mail on your domain (ie: firstname.lastname@example.org or email@example.com). Or you can use a third party service like Google Apps or ZoHo to power your on-domain e-mail.
Shopify only offers e-mail forwarding. You can still have firstname.lastname@example.org via Shopify, but it merely forwards to your regular e-mail address (like your Gmail or Yahoo). So replying to those e-mails comes from your Gmail address, not from email@example.com.
You can still have fully hosted on-domain e-mail with Shopify, but you have to use one of those third party services I mentioned earlier.
Lemonstand does not offer any e-mail services, not even forwarding. You would have to use a third party e-mail provider like Google Apps to receive e-mails at your domain name.
Shopify for providing an easy e-mail forwarding service. But really it’s no big deal to use third party e-mail, and I’d recommend that anyway. I wouldn’t factor this too much into your decision making, as the alternative to setting up e-mail forwards (if you used Lemonstand) is very easy. And you’ll probably want to transition into a service like Google Apps eventually anyway.