A section: Let me weep my cruel fate, and let me breath freedom!
B section: Let sorrow break these chains of my sufferings, for pity's sake.
While the tune is quite simple (and why you hear so many crossover artists are doing it), the range only a 9th and a standard ABA structure, it is the rests that make it sublime. Imagine trying to sob while singing. That seems to be the point Handel was trying to make in the A section. In the B section the vocal line ascends to the 9th as if to imitate the breaking out of the octave of the A section.
If you listen to the other "crying" aria Cara sposa sung by Rinaldo you hear a different type of lament - more controlled with almost a hopefulness or wistfulness that Almirana will return in the A section then a defiance and refusal to accept that she is gone.
The plot of Rinaldo
Libretto by Giacomo Rossi, based on the story of Rinaldo and Armida from Tasso's Gerusalemme Liberata
ClassicalTV program notes detail:
Composed in just two weeks and premiered at the theatre in the Haymarket on 24thFebruary 1711, Rinaldo - Handel's first opera for London - was a triumph. The title role was penned for the great castrato Nicolini, who had recently arrived in England, and Handel aimed to test his range to the full. The piece includes some of his most perfect melodies, including the tender 'Cara sposa' and the bravura 'Venti, turbini'.
The original production was, by all accounts, spectacular in the tradition of the English masque. "Rinaldo is filled with Thunder and Lightning, Illuminations and Fireworks," wrote The Spectator of the day. David Alden's production for the Bavarian State Opera, designed by Paul Steinberg and Buki Shiff, took up the gauntlet thrown down by Handel with the razzle-dazzle of his London coup and this creative team succeeded magnificently in inventing a similarly explosive staging. There are myriad arresting images and special effects.
Because Handel falls into the category of "early music" there can be some discussion on how one sings this aria. I have linked two very different voices singing. Canadian soprano and early music singer Suzie LeBlanc and American soprano Renee Fleming. Two sopranos, two very different sounds and very different ornaments! (please note that they are both appear to be singing at A=415 in original key of F+)
Watch Act I of Rinaldo on ClassicalTV
Get a synopsis from the Academy of Ancient Music
Read what Wikipedia has to say
Aria Database on Lascia ch'io pianga
Buy the aria from Sheet Music Plus