I don’t think the death penalty should be applied if there was no murder. In the examples you cited, what about when women lie? Men have served prison time over false accusing. Would women who commit those acts also be given the death penalty or just men(which violates the equal protection clause)
All that aside, Lois Lerner should be executed for her crimes against the Republic.
She is the worst political criminal in American History
How about identity theft that takes your savings, ruins your life for years?
Firing squad sounds perfect to me.