The key fact in taking taxis in Lima is this: the taxis do not have meters.
In most cities in South America that I have visited or lived in .. either the taxis have meters or they have some other system for determining a fair price between sectors or within a sector.
Lima has neither.
The result is a cat-and-mouse game between the taxistas and their paying customers.
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Here's how the cognoscenti play the game....
Do not enter a Lima cab without knowing what fare you will pay when you exit the taxi.
In my experience, the taxistas usually do not suggest or offer a fare amount when you get in the vehicle.
This is strategic. Once you are inside the taxi and it starts moving without you having established the cost, the taxista believes he has the right to declare the fare later, which may be higher at night or during the busiest times when traffic is the slowest .. or may carry 'the Gringo tax'. You have lost your right to negotiate .. unless you want to get into a Spanish-language confrontation.
If a fare is offered at the outset, you may counter the offer before getting in. Do not allow the driver or honking horns behind you to make you skip this step. Ask the taxi driver to pull over to discuss the fare if necessary.
One way to estimate the proper fare if you are new to the route you will travel .. is to ask a shopkeeper or security officer or cashier what the taxi might charge to get you to your destination.
If you offer five soles and the taxi driver says ten, you might offer seven.
If he won't budge below eight or ten, he may have offered you a fair fare to begin with.
If there is above-average static during the negotiation or along the way, attempt to pay the fare in exact change .. reducing the possibility of a dispute at the end of the ride.
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As you learn how to get around the city, you will discover that some trips are easily and comfortably made at many hours via metro-bus, metro-train or buses on major avenues. Your trip then may cost only one sol, about thirty cents US .. or a sol and a half late at night on Avenida Larco.
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Playing the Taxi Game in Lima
Other taxi items for your consideration....
I prefer official-looking taxis, preferably with a visible number for the cab.
Once you negotiate with a taxista and you cannot agree on a price .. it's your choice whether to wave him on and seek a different cab. If you're in an area with lots of taxis, you can likely get a lower fare from a second or third taxista.
In areas such as around Malecón de la Reserva and Larco, many drivers will seek fares by honking at you or flashing their lights at you if it's after dark. Choose a preferred method to pass on taxis you don't want (lack of markings, second person already in the vehicle, etc.) You can ignore the honk, shake your head no, turn your head away, you get the idea.
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As in many South American cities, many taxis sit or drive around much of the time without a passenger.
This, I believe, is why many taxistas become addicted to their radios.
I usually prefer a tranquilo ride without listening to loud music or Spanish-language debate coming from the radio.
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The keys for a quiet ride are... ask the driver to turn the radio off (or lower the volume) at the start of the trip, even before fully seating yourself .. and try not to be bossy about it. Macho drivers do not like that kind of attitude.
"Hazme el favor de reducir el volumen de la música."
Do me the favor of lowering the volume of the music.
"Me gusta un ambiente tranquilo. Apague la radio, por favor."
I like a quiet environment. Please turn off the radio.
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This is not a Lima thing, but Peru thing, no where in Peru have I encountered metered taxi's, and while shop keepers may be able to give you an average price for a trip, time of day and traffic conditions will always play a part in the fare. When traveling a new route that I do not take regularly, I will generally stop several taxi's to see what price they say, if you get several offering the same price, that is probably the average for that route.
My advice as a Gringo living here for 13+ years
Getting a taxi in Lima is always frustrating. I know they have to eat too but often I feel like Im buying a lot of groceries for them.
I now (often) use 2 different apps to get a taxi. Satelital and Cabify. Dn load them for free on your smartphone. You will know BEFORE you accept their service how much they are going to charge. I have found them to be less expensive on many occasions. The app shows you where they are and estimated time of arrival to your location and their name and a picture of them. There is NO hassell or argument about the price and I have gotten courteous and professional service with both companies. Honestly, I have on a few occasions asked them to drive a little faster. They obey the speed limits and are professional drivers ..... if you can wrap your head around that! If you dont mind walking .... get a card for the Metropolitano. It's cheaper than a taxi and many of the routes will get you close to where you need to go.
The worst place is .... as you ALL have experienced is the AIRPORT. I have a mantra I repeat as I walk across the parking lot. The mantra is NO ..... NO ...... NO the further you get from the door, the cheaper the prices get. You should have an idea by now of the cost from the airport to where youre going. Decide on what you will pay and stick to that price. HAVE THE CORRECT CHANGE. Because its dark or late or the wind is blowing, the price will change when you arrive at your destination so ... Have the correct (agreed upon) fare. I have never had any problem with a taxi but Im a big male gringo. Make sure the door is unlocked before your luggage is loaded in and the driver gets in ...... same for when you get to your destination make sure the driver gets out and is unloading your luggage. Just be smart. Make a quick check to see if you have left anything inside the taxi before exiting. Please dont misunderstand me. I am not indicating all taxi drivers are going to rob you. I hv found the majority to be wonderful people who have to work these late hours to feed their families. Talk to the taxi drivers and you will find THEY are some of the more intelligent people around. Discuss world politics and food with them. You might make a new friend.
If you're a woman traveling alone , you may want to consider paying the higher price and getting one of the official taxi services inside. Welcome to Peru Bienvenidos a Peru. 
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