The reason why the "lan" syllable in Lanfear is thought to be the one meaning daughter is because Siuan gave Min two aliases meaning daughter this and that, and the common syllable in all three is "la".

So it's possible Lanfear litterally translates as night-daughter, but the word order is different from English, ie: it's rather daugher-night.

Bob's on the right track, I think. It's quite possible the "n" (and "m" in other words, it's probably a matter of phonetics) - it is pronounced with a short or long "am" sound in front of vowels, and with "n" sound in front of consonants, and becomes "an" in full, or "'an" when it's a suffi at the end of syllable within a word mark the possessive and some other uses of "of" (as in "betrayer of Hope), a contraction of "an" used when the compound words are expanded into sentences.

It's as if you wrote "(for the) honor of the red eagle" (carai an caldazzar) as caraincaldazzar, which is probably grammatically incorrect, while compounding la'an'fear into Lanfear, or Sa an ael into Sammael, and Isha an ael into Ishamael and Har an into Haran are all correct, maybe because it's not a phrase but compounded names). In languages that aggregate root words into compounds like this, the rules are often fairly elaborate and not always intuitive to speakers of the family of langagues derived from latin/greek that tend to use suffixes and prefixes more than root words, and when we compound words to form another, they usually use the full words, as in "snowball" for "ball of snow". The rules for compounding roots/root words tend to vary from one level of language to the next, eg: between everyday use versus poetry vs religious use). If someone around know, for example, sanskrit (Fionwe?), he/she could explain it much better than I could.

Where it gets a step more complicated is that where to use "of" or the possessive of the/'s doesn' seem to follow the same grammatical rules as english (it seems the grammatical relationship between "Maidens" and "Spear" in Maidens of the Spear isn't the same as in English. It's tied by something else than "of the" in the OT (the word for that appears to be 'mai, or maybe far): the literal translation may be something like : brides/promised to the spear.

In any case, if we knew for sure which langague(s) Jordan used as model, it'd be a lot easier/safer to bring up theories. All we know is that he didn't make all the rules up, or based them just vaguely on languages like Tolkien. Jordan rather borrowed a grammatical structure from one or more existing languages, then he twisted those rules served him to twist existing and invented words. Tuatha'an, for instance, is a twisting following his OT grammatical rules of Tuatha Dé Danaan. In a lot of cases like this, Jordan "cheated", assigning arbitrary meanings to various syllables to obtain words that are very close to names from mythology and legends, to which he gave a different meaning. Aes Sedai, Asha'man, Sammael, Ishamael, Tuatha'an are all examples of this. In the case of Tuatha'an, the word Tuatha (old Irish) means "tribe"/"people" (the full expression means The tribes of the Goddess Ana). Jordan shifted this so "Tu" became his OT word for Travelling/Who travel/nomadic and Atha became people (the final 'an is a plural mark). Then he re used the new word "atha" in other situations, forming for instance Athan Miere (he remained Irish for this one, as Miere is Old Irish for Sea). The vocabulary and "root words" for the Old Tongue comes from all over the map and eras. Jordan's aim wasn't to create a fictitious language so much as contriving a way to get "twisted" versions of real words to fit his "the wheel turns and the same things come and go" concept. The grammatical framework he imposed for the OT made it more coherent, and, I would guess, made it simpler for him to find ways to twists the words/names he wanted. Sooner or later you run out of inspiration for twisting words while remaining coherent. The basic OT grammar he adopted took care of this for him.