What's the role of 一 in 听百灵鸟这么一说，她明白了?
Talking skylarks?? Where are we??
I think you can understand this 一 as 'once' or 'as soon as'
听百灵鸟这么一说，她明白了。
As soon as she heard the skylark speak, she understood.
Once she heard the skylark speak, she understood.
You can also not translate it: Hearing the skylark speak thus, she understood.
Or, to borrow Tang Ho's example:
二人向来不睦，一见面就打架。
Those two are always at odds, as soon as they see each other, they start fighting.