Tense of "lie"/"lay" in a clause

I've been using "lay" but many people have looked at my sentence dubiously.

However, while in secondary school, I abandoned my higher scientific aspirations because I became more focused on a career rather than finding where my personal interests truly lay.

I think I'm trying to use "lie" in past tense, so I used "lay", but is the "finding..." clause present-tense, so does that clash?

No, there is no tense clash. Finding is a gerund here (a verb turned into a noun by adding -ing), and nouns fit with any tense.

You are also correct in supposing that the past tense of lie is lay, though (as FumbleFingers notes below) lie could actually be what you want to use; the present tense would signify that your prevailing personal interests have not changed since then.

Also, I might say finding a job/employment instead of a career, since finding or pursuing a career implies that you are searching out what you want to do; from the context it looks like you mean you found it necessary to take up a job just to make money, not to pursue as a career goal:

However, while in secondary school, I abandoned my higher scientific aspirations because I became more focused on finding a job rather than finding where my personal interests truly lay.