Merhaba  

Ağlama yağmur gözlüm ------ don´t cry my rainy eye

Uyu melek yüzlüm -------- sleep my angel face 

I´ve read these sentences and I was wondering what is the ´L´ exactly  for in the two words ´göz´ and ´yüz´ ?

Can anybody help me in this? 

It is not "l" it is "lü". It is a suffix.

Here is an explanation from http://www.turkishlanguage.co.uk/suffix.htm

The Containing Condition "-li -lı -lü -lu"

The Suffix -li -lı -lü -lu - originating from, furnished with, place of,
This suffix gives the sense of belonging to something or somewhere. It is used with place names - especially to say where one is from. The -li suffix is not separated from a Proper Noun by an apostrophe as other suffixes generally are - "Londra´lı" would be incorrect - Londralı is correct.
Londralı - [Londra-lı] - a Londoner
Londralılar - [Londra-lı-lar] - Londoners
İstanbullu - [İstanbul-lu] - an Istanbuli
İstanbullular - [İstanbul-lu-lar] - Istanbulis
İngiltereliyim - [İngiltere-li-yim] - I am from England
Bolulu - [Bolu-lu] - a person from Bolu
Çinli - [Çin-li] - a Chinese Man (Chinaman)
This suffix also gives the sense of belonging to something or somewhere, it is widely used with place names - especially to say where one is from:
İngiltereliyim - I am from England, Mançesterliyim - I come from Manchester, Nerelisiniz? - Where (exactly) are you from?

An Actual Example of the "containing" suffix.

Here is a picture of a sandwich bar´s billboard showing the type of sandwiches available :

karışık - mixed
kaşarlı [kaşar-lı] - containing hard cheese
sucuklu [sucuk-lu] - containing Turkish type sausage
salamlı [salam-lı] - containing salami
sosisli [sosis-li] - containing sausage
Here vowel harmony is operating on the suffix -li as it has three of it four forms in this picture.

The meaning of - "furnished with" - is used to make attributive adjectives - tuz - salt - giving - tuzlu - salty - is a prime example. Should you use sugar in your tea then you might ask for - şekerli çay - which can mean sweet tea, sugared tea, sugary tea, - according to context.
sabır - patience - sabırlı - patient
kuvvet - strength - kuvvetli - strong
yaprak - leaf - yapraklı - leafy
çimen - lawn - çimenli - having a lawn
yaş - age - yaşlı - old
renk - colour - renkli - coloured
ses - noise - sesli - noisy
yatak - bed - yataklı - furnished with a bed
tuz - salt - tuzlu - salty

Examples
Mehmet sabırlı bir adamdır. - Mehmet is a patient man.
Ali kuvvetli bir genç. - Ali is a strong youth.
Bir yapraklı ağaç. - A leafy tree.
Çimenli bir ev. - It is a house with a lawn.
Yaşlı bir at. - It is an old horse.
İçkili bir lokantaya gittik. - We went to an alcohol serving bistro.
Note: içkili - furnished with alcoholic drinks - [ie: Alcoholic drinks are served]

We can form plural nouns by adding the -ler or -lar plural suffix to an adjective:
sabırlılar - the patient ones
kuvvetliler - the strong ones
yaşlılar - the aged

A typical excellent lesson from www.turkishlanguage.co.uk.

Mr. John Guise is really an ideal language learner: curious, creative, enthusiastic and always ready to pay it forward.