Will an iPhone 5s fit in an iPhone 5c lifeproof case?

No, the skins won't fit. The iphone 5 is 123.8 mm (4.87 in) high, 58.6 mm (2.31 in) wide and 7.6 mm (0.30 in) high. The iphone 5c is 124.4 mm (4.90 in) high, 59.2 mm (2.33 in) wide and 8.97 mm (0.35 in) thick.