Hi Andrew,

You could achieve this by creating a lightning component, use it as a quick action, and in the JS Controller you can redirect to a visual force page.

When you create the component be sure to use

implements="force:lightningQuickAction,force:hasRecordId"

So you can use it as a quick action and also you get the record id to do the process.

Save the record Id in an attribute to manipulate in the component, use:

<aura:attribute name="recordId" type="String" />

Also, you can add a handler so when as soon as the component is loaded you execute a function to redirect

Ex: <aura:handler name="init" value="{!this}" action="c.doInit" />

And in the JS controller the function is something like

doInit : function(component, event, helper) {

var recordId = component.get("v.recordId");

var url = "/apex/nameOfVFpage?parameter="+recordId;

window.open(url, '_self');

}

In case that you need more parameters to send, you might need a function that get those from the server using the record Id that so far is the only attribute you get from the record in a component.

In this case you have to add an Apex controller in the component, and the function must include @AuraEnabled tag so those can be called from a JS controller

Refer here:

Hope this can help you.