This post, and your other one about markets, suggest that you seem to be unaware of what sort of area Park Lane is in!
Park Lane is home to the swankiest of hotels (starting from around £500 per night in many cases), car showrooms which only sell Ferraris, Lamborghinis and similar mega-expensive models and the types of restaurants where even film stars have to book a year in advance and then need to fork out hundreds of pounds for a meal. ('La Gavroche' is just down the road from there and several celebrity chefs have their restaurants in the area).
You simply won't find any markets or Greek restaurants around there. (You'd struggle even to find a pub in that part of London, although there are plenty of expensive champagne bars and cocktail lounges).
Although this is your 'Greek restaurant' thread, I'll try to help with the 'markets' bit first. Take a look at this map:
http://www.streetsensation.co.uk/markets.htm
The green bit below Lancaster Gate tube station is Hyde Park. The road which runs down the eastern side of Hyde Park is Park Lane. (NB: Hyde Park, including Kensington Gardens is 1½ miles long. That will give you a sense of scale!). The locations of some of London's principal markets are shown on the map, together with a brief description of each one. (Unless you're a very keen walker, you'd need to take a bus or the Tube to access any of them).
Once you've got a general sense of the relevant geography, this map provides far more detail:
http://londonist.com/2014/12/markets-in-london-mapped
One of London's best markets (in my opinion) is Borough Market. It's open from Monday to Saturday but there aren't many stalls open on Mondays & Tuesdays. (Wednesday to Saturday is best):
http://boroughmarket.org.uk/
(From Park Lane, walk to Green Park station and take a Jubilee Line train, for 4 stops, to London Bridge)
Shepherd's Bush Market always seems to have a traditional 'East End' feel to it to me (despite it being located in West London!) and it's well worth a visit:
http://myshepherdsbushmarket.com/
(From Park Lane, go to Hyde Park Corner station and take a Piccadilly Line train for 6 stops to Hammersmith. It's walkable from there or you can take a Hammersmith & City Line train, for 1or 2 stops, to either Goldhawk Road or Shepherd's Bush Market)
For Greek restaurants in London, TripAdvisor is a good place to start:
https://www.tripadvisor.co.uk/Restaurants-g186338-c23-London_England.html
I note, in particular, that branches of The Real Greek figure prominently throughout that list:
http://www.therealgreek.com/
(The St Martin's Lane branch is probably the easiest to access from Park Lane. Take a Central Line train from Hyde Park Corner, for 3 stops, to Leicester Square).