It really is the same old "be careful" routine. Avoid flashy jewellry and wallets in easy-to-pickpocket places, stick to the better areas and, if you're walking around at night, take $200 cash and nothing else...that will leave the mugger satisfied, and you'll be little worse for the wear.
I lived for four years in Peru (until mid-2004) and I was never robbed. Not to say that it can't happen, but with basic precautions the risk is quite manageable. And Lima has improved a lot since the 80s, so travel and enjoy!