Does “lay it on the line” mean "frankly speaking"? If so, can I use "speak frankly” instead?
Yes, it is! To be more specific, the idiom "lay sth on the line" stands for "risk sth" and "to say in a direct or honest way. (even if this might upset someone)" It was used as "to say it direct way" in this fragment. As you've asked, this idiom can be replaced with "speak frankly, speak honestly" Ex: Let me lay it on the line to you, if your work doesn't improve, you'll be fired. Ex: It's time to lay it on the line and tell her the truth about his past. Ex: I'd be laying my life on the line by giving you that secret intelligence.