Is the statement "There's a reason for everything" a soothing lie we tell ourselves?
Yes and no.
This statement is usually made in the context of spiritual awakening, and it is, in itself, a spiritual statement. Spirituality is a vehicle to discover the truth of your nature, it is not the truth of your nature. When the truth is discovered, spirituality is abandoned.
During the unfolding it certainly feels this way, and the closer one is to the realization, the truer this statement feels. But it is not true in the absolute sense.
A much more correct statement would be: “There is no reason for anything that’s happening, but there’s a reason for everything you feel about what’s happening”.
Life is chaos, it’s unpredictable and cannot be predicted. But our perception of life is not chaotic, it is deeply rooted in our subconscious beliefs about ourselves and others, morality, notions of right and wrong etc. That’s why it feels like there’s a reason for things that are happening to you. It can feel almost like life is trying to teach you a lesson, and it is, in a way - the lesson being that none of those beliefs are true, and the best you can do is just accept the chaos and not try to comprehend it or build a personal story around it with all the reasons for why it was that way. When such acceptance happens in totality, that’s enlightenment.