Peruvian lily is the common name for Alstroemeria - put Alstroemeria into Google and select images.

Be aware that they may take a year or two to become established. Mine did but now, after three years, they are doing well and no trouble. When you take off the flowering stems never cut....only pull. That way you may have another flowering show. They make wonderful cut flowers.

Generally, the stems that are going to bloom end in a tight, irregular cluster of rugby ball-shaped buds. Non-blooming stems show nothing at the ends. No spikes involved in either case. Do you have pictures?