My 2003 Civic (1.7L) with 23K miles has started knocking briefly on startup on very cold (20 degrees or colder) mornings. I starts and runs ok for 3 or 4 seconds, then makes a knocking sound for approx 5 seconds and then the sound fades away and it runs fine. It sounds like it's more than a lifter, perhaps a rod? The frequency is 3-5 times per second.
I'm running Amsoil synthetic 0W/30 with a Mobil1 filter and this started shorlty after I switched from Amsoil 5W/30, but that's also when the really cold weather started.