In Part 2, the presentation of the 7-7-7 Lamech Prophecy began with the meanings of the names of the descendants of Adam in Genesis 5. They appeared to spell out a prophetic messianic message:

"A man (is) appointed mortal sorrow. Praise of God! He shall come down teaching, (that his) death shall bring the despairing, rest!"

As much as I would like to believe this, is there a Hebrew dictionary or Lexicon out there that corroborates these meanings behind the names? If so I would love to know it because I have had a difficult time verifying the validity of a number of the names.

This is what Strong's Concordance gave me; I looked at not only the names but the root words as well:

Adam: red (H121); man, mankind (H120) - strongly agrees with "man"

Seth: compensation (H8352); to put, set (H7896) - loosely agrees with "appointed"

Enosh: man (h583); man, mortal man, person, mankind (H582); to be weak, sick, frail (H605) - agrees with "mortal"

Cainan (Kenan): possession (H7018); nest (H7064); to make a nest (H7077) - does not agree with "sorrow"

Mahalalel: praise of God (H4111); praise, boast (H4110; to shine (H1984) - strongly agrees with "praise of God"

Jared: descent (H3382); to go down, descend (H3381) - strongly agrees with "he shall come down"

Enoch: dedicated (H2585); to train, dedicate, inaugurate (H2596) - loosely agrees with "teaching"

Methuselah: man of the dart (H4968); male, man (H4962); weapon, missile, sprout (H7973); to send, send away, let go, stretch out (H7971) - strongly disagrees with "death shall bring"

Lamech: powerful (H3929) - strongly disagrees with "the despairing"

Noah: rest (H5146); resting place (H5118); to rest (H5117) - strongly agrees with "rest"

As you can see, most of the names appear to agree except for these:

Cainan (Kenan)
Methuselah
Lamech

And of the names that do agree, these seem to be a bit of a stretch:

Seth
Enoch

I want another source besides Strong's but haven't had much success in finding one.

Cainan (Kenan)
Cainan is a difficult one. It is not a word used often. The name Qeynan comes from the verbal root קנן (qanan, Strong's #7077), literally meaning "to make a nest." This verbal root is derived from the parent root קן (qeyn, Strong's #7064) meaning a "nest." Qeynan (קינן) can mean to possess and it can mean to mourn, lament or sorrow after (see Ezekiel 27:32 and Amos 8:10).

Methuselah
This name is pronounced meh-tu-sheh-lahh (the "hh" is pronounced hard like the "ch" in the name "Bach") in Hebrew. This name is a combination of two words - metu and shelahh. Strong's dictionary states that this name means "man of the dart". According to Strong, the root for metu is the word mat (#4962) which means "man" and the word shelach (#7973) means a weapon or missile (hence the translation of dart).

But, there is another possible meaning for this name. The word metu may be derived from the word mot meaning death and the "u" is a suffix that means "their" - "their death". There is no way to know for certain if the final vowel in metu was an "o" or an "u" as the vowel pointings that make that distinction are of fairly recent origin. If it was originally an "o" then the suffix would change to "his" - "his death".

The word shelach (missile or weapon) is the noun form of the verb shalach meaning "to send" (a missile or weapon that is sent). Shelach has the more literal meaning of "to send something".

We know have the possible meaning of "their death sends" or "his death sends". Sounds like an incomplete sentence doesn't it? Well, it is interesting to note that the year Methuselah died, something very big was sent - the flood. Methuselah's name may be a prophecy that on the day of his death "his death will send" the flood.

Lamech
This is one of the names in the Bible that is very difficult to translate as the root of this word, למך, is not used anywhere in the Biblical text and therefore the meaning of this root/word/name is impossible to determine with any degree of accuracy. One possible interpretation is that this name is the verb מוך (mok, Strong's #4134) meaning "low" and prefixed by the letter ל meaning "to" – "to be low" i.e despairing. Other lesser often suggested meanings for this root/word/name are powerful, robust and priest.

Strongs is not really a great tool to use for the meaning of a Greek or Hebrew words, as it is really just a concordance.