What you should do is follow this example and use AMPscript in your subject.
"inArguments":[
{ "firstName":"{{Contact.Attribute.__your-de-name__.FirstName}}"},
{ "lastName":"{{Contact.Attribute.__your-de-name__.LastName}}"},
{ "emailAddress": "{{Contact.Default.Email}}"}
],
When you fire the event, you can pass data into the DE to be saved. Your custom activity can receive inArgument data to be used within the custom activity. A standard activity like Send Email can pull in DE data via AMPscript.
Also, see this question/answer/commentsquestion/answer/comments for more information.