There is a belief, that a free lead-magnet is the best option for having high conversion. But why don't you try to make your "free" product free only for some period of time, after which you'd set some price for it?
For example, let's imagine you have an e-book which is your lead-magnet. Instead of giving it everybody for free, state that it will only be free for those who downloads it within a month, and then it'll cost $9,99. This will motivate people to instantly leave their emails, because they'll know that otherwise they'll have to pay for this book later.
To make you time limited offers attract even more clients, follow these steps.
1. Make a good offer.
2. Show this offer to the right people.
3. Motivate them to act here and now!