Details of Georges Lemaître's life are checked here.

From wikipedia, Georges Lemaître:

In this report, he presented his new idea of an expanding universe, derived from Hubble's law, and provided the first observational estimation of the Hubble constant[11] but not yet that of the primeval atom. Instead, the initial state was taken as Einstein's own finite-size static universe model. The paper had little impact because the journal in which it was published was not widely read by astronomers outside Belgium; Arthur Eddington reportedly helped translate his article into English in 1931, but the part of it pertaining to the estimation of the "Hubble constant" was not included in the translation for reasons that have never been properly explained.[12]

From 'A Day Without Yesterday': Georges Lemaitre & the Big Bang:

 Sir Arthur Eddington volunteered to work out a solution. When Lemaitre read of these proceedings, he sent Eddington a copy of his 1927 paper. The British astronomer realized that Lemaitre had bridged the gap between observation and theory. At Eddington's suggestion, the Royal Astronomical Society published an English translation of Lemaitre's paper in its Monthly Notices of March 1931.

Was Lemaitre's work derived from Hubbles?

The record is set straight on this by M.J. Way (NASA/GISS), Harry Nussbaumer (ETH, Switzerland) in Lemaître's Hubble relationship published in Physics Today, August 2011. 

Friedman (1922) was the first to publish non-static solutions to Albert Einstein’s field equations. However, he did not extend that into a cosmological model built on astronomical observations. Some five years later, Georges Lemaitre also discovered dynamical solutions (Lemaˆıtre 1927). In the same publication in which he reported his discovery, he extracted (on theoretical grounds) the linear relationship between velocity v and distance r: v =Hr. Combining redshifts published by Str¨omberg (1925) (who relied mostly on redshifts from Vesto Slipher (e.g. Slipher 1917)) and Hubble’s distances from magnitudes (Hubble 1926), he calculated two values for the “Hubble constant” H, 575 and 670 km sec−1 Mpc−1 , depending on how the data is grouped. Lemaˆıtre concluded from those results that the Universe was expanding. Two years later Hubble found the same velocity–distance relationship on observational grounds (Hubble 1929) from practically the same observations that Lemaˆıtre had used. However, Hubble did not credit anyone for the redshifts, most of which again came from Slipher.

In other words, Lemaitre first came up with "Hubble's Law" and first came up with some values for "Hubble's constant", before Hubble did, but they bear Hubble's name not Lemaitre's.

This is acknowledged in the wikipedia article on Hubble's Law:

Although widely attributed to Edwin Hubble, the law was first derived from the general relativity equations by Georges Lemaître in a 1927 article where he proposed the expansion of the universe and suggested an estimated value of the rate of expansion, now called the Hubble constant.[5][6][7] Two years later Edwin Hubble confirmed the existence of that law and determined a more accurate value for the constant that now bears his name.[8] Hubble inferred the recession velocity of the objects from their redshifts, many of which were earlier measured and related to velocity by Vesto Slipher in 1917.[9][10][11][12]

There is no mention of Eddington realising Lemaitre was right. Here are two academic sources that confirms Eddington's affirmation of Lemaitre's break through.

The Expansion of the Universe: Who Discovered the Expanding Universe? What was Really Discovered? in The CAAUL Gazette: The International Newsletter of the Centre for Astronomy and Astrophysics of the University of Lisbon

Eddington, working on the problem of instability of Einstein’s static model, came across the Lemaître paper, and found in it the solution of its own problem. 

Dismantling Hubble’s Legacy? by Michael J. Way on NASA Technical Reports Server

Eddington took part in this project in important ways that did not include actual “discoveries”: 1. He participated in a number of important discussions with most of the authors listed in Table 3.41 2. He was responsible for the re-publication and translation of Lemaˆıtre’s 1927 paper in Monthly Notices of the Royal Astronomical Society (Lemaˆıtre 1931). He initially brought Lemaˆıtre’s work to the attention of the world in his May 1930 paper (Eddington 1930). ... Overall we find that Lemaˆıtre was the first to seek and find a linear relation between distance and velocity in the context of an expanding universe.

Clearly Eddington 'found' the paper (or was sent it by Lemaitre - I'd have to read those books which are the basis for this history to solve that one) and realised Lemaitre was right. The Catholic article is closer to the truth than wikipedia about Lemaitre's discovery of the big bang.

Side note: on why the English translation is missing the crucial part: Lost in translation: Mystery of the missing text solved

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Fr Georges Lemaitre first came up with "Hubble's Law" and first came up with some values for "Hubble's constant", before Hubble did, but they bear Hubble's name not Lemaitre's.

Fr Georges Lemaitre first developed the Big Bang theory.