[一 + v] = [once /upon + v]
听百灵鸟这么说,她明白了 = After hearing the lark said it like that, she understood
(一)听百灵鸟这么说,她明白了 = (Upon) hearing the lark said it like that, she understood
听百灵鸟这么(一)说,她明白了 = Hear the lark (once) said it like that, she understood
It would be easier to understand if we omit 听 and write: "百灵鸟这么一说,她明白了" = "The lark once said it like that, she understood" ("heard" is implied)
Note: depend on context [一 + v + 就...] can mean [once + verb + then...] or [would + verb + every time]
Example:
一見面就打架 = "Start fighting upon seeing each other" or "They fight every time upon seeing each other"
不知如何,這兩人一見面就打架 = For an unknown reason, the two started fighting upon seeing each other"
二人向來不睦,一見面就打架 = The two have not been friendly to each other, and they fight every time they meet"