What tool are you using? Probably a way to go could be using Segment.io. By using Segment or (Analytics.js) you won't depend on a specific tool. Anyway, you could treat every new signup as a trial user unless proved the opposite. So you call new user a lead. Then you register a purchase event when it happens. Purchased/Leads would be the conversion you are looking for. Heap, Mixpanel allow you to do so.
What tool are you using? Probably a way to go could be using Segment.io. By using Segment or (Analytics.js) you won't depend on a specific tool. Anyway, you could treat every new signup as a trial user unless proved the opposite. So you call new user a lead. Then you register a purchase event when it happens. Purchased/Leads would be the conversion you are looking for. Heap, Mixpanel allow you to do so.