If you want to bring your cell phone with you to Lima, make sure it works in Peru. To avoid frequency compatibility problems best have a GSM multi-band phone. While you can use your SIM card from home, be aware of high roaming charges. To avoid these fees, you can buy a quite inexpensive local pre-paid SIM card (incl. Internet, e-mail... for smart-phone users) directly at Jorge Chavez International Airport which you can exchange for your original one as long as you have an unlocked cell.
Another option is to rent a local mobile phone incl. a local SIM card at the airport. You can choose between Claro, Movistar, Nextel and Rent a cell. Just have a chat with the nice young ladies waiting for potential customers before you get your luggage and pick a plan that best suits your needs. Be aware that prices can be steep. Ask for connection fees, other charges and penalties! Read the fine print before you sign anything!
Even though it's required by Peruvian law to be a legal residents, there are still numerous cellphone shops around town selling you a cheap pre-paid cell only with your passport and a local address (your hotel). Most often this option is less hassle and much cheaper.