Is Soapbox Mailer compatible with Salesforce's new Lightning Experience?

Yes, Soapbox Mailer is compatible with Salesforce Lightning.

Salesforce "Lightning Experience" is a slick new user interface layered on top of your existing Salesforce account that focuses on allowing sales teams (or development and fundraising teams in our nonprofit community) work and close opportunities faster. It is generally available as a feature that can be enabled by Salesforce administrators starting with the Winter '16 release. 

While we're very excited about this new functionality, there are some key Salesforce features that are not yet supported including some critical ones for Soapbox Mailer such as: 

• No support for campaign and campaign member data (coming in Spring '16
• No custom buttons
• No ability to search for duplicate Leads or add Leads to Campaigns
• And more...see the full list here

If you enable the Lightning Experience, you will need to switch back to Salesforce Classic in order to be able to send Soapbox Mailer campaigns and view Campaign Member histories. 

For more considerations on rolling out the Lightning Experience, we highly recommend checking out the Trailhead module called "Is the Lightning Experience Right for Me?"