A paid growth engine is basically standard marketing, investments results in more exposure which should lead to more customers.
Acquired customer price
It is of course important that the price of a new customer is lower than the generated revenue from acquiring said customer.
Reference
Ries, Eric. The Lean Startup: How Today’s Entrepreneurs Use Continuous Innovation to Create Radically Successful Businesses. 1st ed, Crown Business, 2011.
Highlights or timestamps
Finally, a paid engine works by investing into marketing, for example through paid online advertising. Of course, this is only sustainable if existing customers bring in enough revenues to ensure the costs per user acquisition are lower than user lifetime value.
— ^222f00 from The Lean Startup