Three days is enough time to see something of Lima although it's a very large city with a lot to see and do, so you could easily spend more time there. You should budget one day (and an evening) for the historical center of the city, with the churches etc., and if you're there in mid-summer then at least one day to the beaches south of the city is recommended (Playa Santa María is a nice, sheltered beach that I enjoy, but there are many others including excellent beaches at Asia about 100 km south of the city). Also districts like Barranco are a must see, and there's a lot of good shopping for Peruvian crafts and the like, but the best stores are scattered throughout the city so it takes time to get around to them all.

If you're like me and you travel mainly for the food, then you should plan the longest stay possible in Lima. Perú's cuisine is truly a delight. Try the top end cebicherías for a fanstastic seafood lunch, and any one of a huge variety of good restaurants for dinner.

Enjoy!