This was a bit of a challange.
All the information is pretty much the same as Stan commented above.
比喻行踪漂泊不定的人。 清 黄景仁 《稚存从新安归作此寄之》诗：“来鸿去燕江干路，露宿风飞各朝暮。”
None of this really answers the question though. Searches for 来鸿去燕 don't elaborate at all and that's just the problem - it's so easy to over-complicate Chinese; what originally was very simple is very easily complicated by our strange minds.
So let's look at this as simply as we can:
We have 来。。。去。。。a very simple + common construct "to come & to go"
鸿 & 燕
So let's look in the dictionary for 鸿燕:
鸿雁和燕子。两者均为候鸟。于 长江 一带, 前者秋来春去, 后者秋去春来。
Swan goose & swallow. Two migratory birds. Along the Yangtze River the swan goose comes in the autumn and leaves in the spring, the swallow leaves in the autumn and comes in the spring.
清 方文 《芜阴送钱既白游太湖》诗
我方來爾邑, 爾復去吾鄉。交錯如鴻燕, 拼飛爲稻粱。
We can see the usage here:
Zigzagging like swans and swallows.
So you can get the feel of the "one comes" the "other leaves" concept.
So we can see 来鸿去燕 is kind of like zigzagging all over the place - leaving and going - coming and going.