In Houston we have humidity issues year round, so I worry about the same thing. My first two bottles of lye were bought at Lowe's. The very first one was small and used up very quickly, so there was no time for it to get clumpy or show signs of moisture impact. But the second bottle, which was used more slowly, definitely began showing signs of moisture impact as the muggy summer heat managed to infiltrate everything, despite the AC being on at all times. As soon as I saw the crusty lye on the rim of the opening, the clumps when I poured, etc, I disposed of it and ordered more.
My solution since then is to store my lye bottles in giant Ziploc bags. Whether I've opened them or not, I put the bottle in the Ziploc, push the air out, and zip closed. This has proven to be effective for me at least. No more crusty lye or clumps.