When you have a prefix, such as a lamed, before the name YKVK people pronounce it la | donai instead of la | a | donai. Why?
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 For this particular rule he references an unpublished lecture by M. Zanitsky (Dikduk Lectures) from 1989.
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."
When the letters Mem Shin or Heh are used in the beginning of the word, the following sound will be vocalized or will be brought out and pronounced. This is the meaning of Moshe (a short way of saying Mem Shin or Heh) Motzi (is brought out or pronounced). This is in contrast to the letters Kaf Lamed or Beis that do not cause the following letters to be pronounced when they are used in the beginning of the word. Kalev ( a short way of saying Kaf Lamed or Beis) Machnis (gathers in the sound).
Towards Better Davening and Torah Reading Column #116 Contents of this weekly column are (mostly) based on the sefer: EIM LAMIKRA HASHALEIM by R' Nissan Sharoni, Ashdod, a guide to correct pronunciation of Hebrew, specifically in davening and Torah reading. Moshe keeps it and Kalev swallows. Doesn't rally mean anything, but the Hebrew phrase is a mnemonic device, as follows. MOSHE MOTZI V'KALEV MACHNIS Here's what it means. G-d's "main" Name, whether spelled YUD-KEI-VAV-KEI or ALEF-DALET-NUN-YUD is pronounced ADONOI, the first letter being ALEF with a CHATAF-PATACH under it. ELOKIM or any of its variations (ELOKEINU, ELOKE- CHA, etc.) begin with ALEF with a CHATAF-SEGOL under it. When one of these names has a prefix of a BET, HEI, KAF, LAMED, MEM, or SHIN, sometimes the sound of the ALEF drops and sometimes it doesn't. Specifically, with MEM, SHIN, or HEI, the ALEF's vowel remains. That's the meaning of MOSHE MOTZI, with the letters of the name MOSHE, the sound of the ALEF emerges. With VAV, KAF, LAMED, or BET (letters of V'KALEV), the ALEF's vowel is swallowed - i.e. dropped. Check out these examples: SHE-ADO...ASHERI H'AM SH'HASHEM ELOKAV MEI-ADO... M'HASHEM YATZA HA'DAVAR but, BA-DO (not B'ADO)...VA'YA'MINU BA'HASHEM and, LA-DO... MINCHA L'HASHEM The same rule applies to "master" when not referring to HaShem. Sarah said: i¥e²z h°b«st³u, that's VADONI, not VA-ADONI. HA-ELOKIM, but LEI-LOKIM. There are 7 exceptions in Tanach to this rule.
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":
An exception (among others) is the word ADON which is too small to have its ALEF go silent. So we say, ALEINU L’SHABEI’ACH LA-ADON HAKOL, not LADON.
It should be noted that while the Moshe Motzi rule generally applies, it is NOT universal. There are a number of exceptions in Tanakh:
R’ Sharoni also lists seven exceptions found in Tanach, including VA-ADONEI HA-ADONIM (D’varim 10:17), LA-ADONEIHEM L’MELECH MITZRAYIM (B’reishit 40:1), KI KADOSH HAYOM LA-ADONEINU (Nechemya 8:10, and not LADO- NEINU as the rule would have it). Also, if the LAMED or BET has a KAMATZ under it, then it is doubling for itself and HEI HAYEDI’A, the definitive article HEI. In that case, the vowel of the ALEF is NOT dropped and the ALEF does not go silent. Sh’mot 22:19 forbids sacrificing to any deity besides HaShem. ZOVEI’ACH LA-ELOHIM. Here the LAMED is “to” and “the”, as if it were L’HA-ELOHIM (acheirim) and the ALEF remains sounded. Similarly, EIN KAMOCHA BA-ELOHIM HASHEM...