When you have a prefix, such as a lamed, before the name YKVK people pronounce it la | donai instead of la | a | donai. Why?
This rule applies not only to the lamed prefix, but also to vav, kaf, and bais. My understanding/conjecture is that the obscuring of the chataf in the Shem Hashem is to make clear that the patach under the prefix is not indicative of the definite article.
To explain: The prefix ה generally serves as the definite article ("the") in Hebrew, but when there is another prefix (such as lamed) the ה is omitted, and instead the other prefix gets a patach (e.g. la-shulchan instead of l'ha'shulchan). Now, whenever any form of the definite article is used, it is implicit that the subject is not unique. For example, I may say that I am the Dave, which implicitly excludes all others who may call themselves Dave. But this is not appropriate when referring to Hashem, since he is One and unique. Using the definite article when referring to Hashem would be heretical (borderline, a least)!
So, if one were to say la-ado-nai, it could be interpreted as meaning "the Hashem," which we do not want to do, as explained above. Rather, we say la-do-nai, so that it is clear that the patach is serving merely as a grammatical replacement for a shva.
I think this derives from the rule "Moshe Motzi Kalev Machnis."
Interestingly is how this applies to the word "Master" that does not refer to G-d.
For a list of pronunciation's of G-d's name, see the Stone Chumash.
As to the mystery of why La'Adon is not L'Adon in Aleinu, the only answer I can find thus far is that it is simply "too small":
It should be noted that while the Moshe Motzi rule generally applies, it is NOT universal. There are a number of exceptions in Tanakh:
From the book in English, "The Complete Torah Reading Handbook," by Dr. Ely Simon, Judaica Press, New York, 1996, page 43:
Dr. Simon says there is a rule about this, and the rule is that for the prefixes ו,כ,ל,ב the א (in all Names of Hashem that begin with an alef) is supressed by the prefix and its vowel. The same rule applies when the term אדון is used for mere human masters or rulers and the term אלהים is used for judges or other important people, too.
The other half of the rule is that the prefixes מ,ש,ה do not supress the initial alef, and the alef keeps its vowel and is pronounced.
There is a mnemonic for this rule: משה מפיק וכלב מכניס, which Dr. Simon translates as "Moshe speaks (the words of G-d) eloquently, and Calev brings (the people) in (to the Land of Israel)."
Dr. Simon does not provide any specific grammatical reason other than stating that this is the rule whenever the name of lordship with an initial alef is preceded by these particular prefixes. For this particular rule he references an unpublished lecture by M. Zanitsky (Dikduk Lectures) from 1989.