Usually I make lasagna bolognese with bechamel, but am in a bit of a time crunch and decided to go with ricotta instead. I folded in roughly equal parts by volume grated parmigiano reggiano and grated pecorino romano into the ricotta. Some online sources state that egg(s) are required, otherwise the ricotta will become runny; others say there is no difference. Given the amount of dry cheese that went into the mixture, will there be any problems with runniness? Thank you so much for your insights!