If you don't want to use the inbuilt LC Email system in Growably (what is LC Email?) and want to use your own SMTP Provider, then Mailgun is the next best option as it has the deepest integration.
There’s two ways to integrate Mailgun into Growably:
OPTION 1: The API Method
This is the slightly slower, but better method using your own Mailgun account
The reason it’s better is because it is a deeper integration which gives you more email sending stats in Growably (such as Bounce Rates etc).
The reason it’s slightly slower is that you need to securely send us your Mailgun API Key and wait for us to add it into your account in our Admin Portal.
This takes us about 1-2 business days.
Click here for the secure form to send us your API Key.
IMPORTANT
At the moment, the High-Level Mailgun integration only works for domains setup in the US region.
If you setup your domain in the EU region, it will not work.
If you aren't able to setup your domain in the US region due to your GDPR Policy, then you will need to use OPTION 2: The Direct SMTP Method below.
Once we securely receive your API key, we’ll add it within two (2) business days and let you know once it's added.
Make sure to setup all the DNS Records that Mailgun lists during the process of setting up your domain/sub-domain in your Mailgun account.
We also strongly recommend you configure your DMARC policy for this sub-domain to either quarantine or reject (preferred).
(and before you ask, yes – we’ve already asked High-Level to build a system to allow you to do this yourself without us being stuck in the middle handling API keys 
)
OPTION 2: The Direct SMTP Method
This second option is the quickest yet not full featured method.
It’s the quickest because you can set it up immediately and start using it.
The reason it’s not full featured is because it doesn’t have deep statistical integration into Growably so you won’t be able to see stats like Bounces Rates etc.
This method literally just allows you to send emails via SMTP.
To configure this option, go to your Growably Settings section and select the Email Services option, click the Add Service button and choose Other.
Then just fill in all the SMTP details on the page and you’re good to go.
What is a Sub-Domain
Check out this article to help work you decide whether you are going to use use a Primary Domain or Sub-Domain when emailing out of Growably.