There are 4 times in parshat Chayeii Sarah that the events at the well are related:
The first is 24:14 (English from the chabad website) - what Eliezer prays for
And it will be, [that] the maiden to whom I will say, 'Lower your pitcher and I will drink,' and she will say, 'Drink, and I will also water your camels,' her have You designated for Your servant, for Isaac, and through her may I know that You have performed loving kindness with my master."
The second is what actually happens (17-20)
And the servant ran toward her, and he said, "Please let me sip a little water from your pitcher." And she said, "Drink, my lord." And she hastened and lowered her pitcher to her hand, and she gave him to drink. And she finished giving him to drink, and she said, "I will also draw for your camels, until they will have finished drinking." And she hastened, and she emptied her pitcher into the trough, and she ran again to the well to draw water, and she drew for all his camels.
The third is during the recap when Eliezer says what he was looking for (24:43-44)
Behold, I am standing by the water fountain. When a maiden comes out to draw [water], I will say to her, 'Please, give me a little water to drink from your pitcher.' And [if] she will say to me, 'You too may drink, and I will also draw water for your camels,' she is the woman whom the Lord has designated for my master's son.'
And finally when Eliezer says what actually happened (45-46):
I had not yet finished speaking thus in my heart, and behold, Rebecca came out with her pitcher on her shoulder, and she went down to the fountain and drew water, and I said to her, 'Please give me to drink.' And she hastened and lowered her pitcher from upon her, and she said, 'Drink, and I will also water your camels.' So I drank, and she also watered the camels.
In 3 of the versions, the woman is presented as responding to a single request for water as immediately offering the man water and the camels water. However, in the actual event (version 2) she only offered to water the camels after he finished drinking.
This series of events is commented on in the Artscroll as being the better way -- had she offered to water the camels at first, Eliezer might have rushed to drink or reduced how much he drank (the chumash on page 113 references the Or HaChaim). Her not initially offering to water the camels is a positive thing!
Why then would Eliezer not retell the events in version 4 as they actually happened? Why change it to be in line with the 2 prayer-versions of immediate help? Why lie and lie in a way which detracts from the wonderful thing that she did?