live in hope that
（在不太可能的情况下）对…继续抱有希望，痴心妄想
If you live in hope that something will happen, you continue to hope that it will happen, although it seems unlikely, and you realize that you are being foolish.
I just live in hope that one day she'll talk to me.
我只是妄想着有一天她会和我说话。
The situation is not good but we live in hope that it will improve.
情况不好，但我们依然希望会好转。
当然，可以转化为：live in hope of （doing）sth.
My mother bought lots of tickets and lived in hope of winning the prize.
我母亲买了很多彩票，一心希望能中大奖。《柯林斯高阶英汉双解学习词典》
All through the winter, we live in hopes of warmer weather.
整个冬天，我们都希望有较为温暖的天气出现。
But he lived in hope of a return of national footballing confidence.
但是他还是心存希望，希望有朝一日印度足球重整旗鼓。
I live in the hope of meeting with him, but this meeting is not yet.
我苦苦希望与他相见，但是这相见的时间还未到来。