An old mechanic's trick, you don't need a stethoscope but they are nice. Take a long screwdriver and place it on the spot you want to hear. Put the handle end against your head and just in front of your ear. The sounds will get into your ear by conduction. Good for pinpointing bad bearings, wrist pin slap, loose valves, etc. Next time you change your oil, before you dump the old oil, run the motor with some engine flush to remove the varnish in the lifters. The reason the noise goes away once it warms up is because the varnish softens when hot. The engine flush washes away the varnish. Any large auto store will have some. Follow the directions and then change the oil AND the filter.
@esprit888 - I agree, it looks like the smooth side of the belt is rubbing against a grooved pulley, but I’ve looked at every contact point and am certain that’s not what’s causing it. The indentations are much closer together than the groves on the pulleys, plus they’re really shallow. It’s not getting any worse, so I’m going to buy a new belt and keep an eye on it. @Add Lightness - the tapping was so loud I was certain a valve was smacking into a piston, which kinda freaked me out. Lesson learned, next time I‘ll let it run a bit before I panic. At the end of the day I’m not sure I even needed to change the belts. Sure, they were eight years old, but they look perfect. The serpentine belt was cracked all over the inside, so I’m glad I replaced it. All the bearings were turning freely, I’m not sure they needed to be replaced either. I’d love to send the belts out to have them tested to see how much life is left in them. I know belt change intervals are a hot topic, but I’ve yet to hear definitive info on how long the Gates blue belts should last. Lotus changed their guidance several times, so maybe no one really knows… my plan is to run the new belts at least five years, maybe seven depending on my tolerance for the risk of them breaking. @jtrealty - do you have a recommendation on which engine flush to use? I‘ve never used them.
At eight years you were wise to change the belts. Could have gone more... or not. Pretty cheap insurance and the knowledge you gained about your engine is priceless. Lacking truly certified Lotus training on your engine any information you are getting on here is from people who learned just like you, some with professional mechanic experience and some (like me) without. Just keep learning and you'll have the answer for someone else too.
Agree, you would have to get very creative to wrap the back of the belt around a grooved pulley, but seen it done several times on the Audi engines. On the V8 the smooth back side of the belt should only wrap around the tensioner pulley.