If it's scale, you'll have to pick them off with your fingers, and then use the soap and water (a few drops of dish soap in water, pref.)to eliminate the more immature scale that are not yet covered by the tough shell...have you seen pictures of scale? They cover themselves with a roundish, tan-to-black hard shell (that protects them from anything you put on) and then remain stationary on the
plant, sucking it's life juices. This shell is what you scrape off with your nails, then you can treat the
plant. Whether it's scale or aphids, I would recommend adding some rubbing alcohol (1 part, to 3 parts water) to the mixture to make it stronger. Diluted alcohol won't hurt most
plants, and definitely not a spider, though I'm not positive about the lime. You'll want to repeat the application, maybe twice a week for a month.