Yes, limewater is indeed strongly alkaline, but it can get depleted quickly because of the low concentration/solubility of calcium hydroxide - better not filter off the excess Ca(OH)2 for most purposes.

I did a little STB experiment years ago with a warm lime 'slurry' instead of lye, with powdered MHRB... yield was rather low but very high purity, snowwhite crystals in one go!