Hey JamesH, welcome to the forum my man!
The Lidl (
website 
) I go to (and the nearest to Sol) is right smack dab in the middle of Plaza de Tirso de Molina (#15-17) just south of Plaza de Jacinto Benavente which is just south of Puerta del Sol.
From Sol, take Calle Caretas South to Plaza Jacinto Benavente, cross the Plaza and take Calle Doctor Cortezo South along side "Cine Ideal" (Yelmo Cineplex movie theater) and when you hit the end you are in Plaza de Tirso de Molina. Make a right and walk about 200 yars, Lidl is on your right.
The supermarket is on the North side of the Plaza and ya can't miss it.
You can see the yellow of the store sign hiding behind the tree at lower right in
THIS PHOTO FROM QDQ. You can also see part of it at lower left in the shot of Plaza Tirso de Moiina #17
HERE 
(right next to the Apolo Restaurant).
I go there for some things I can't get at D�a as well
Happy shopping.
Saludos & see ya around,
jer...