Understanding theological poetry like this requires a lot more than knowledge of grammar. There is a whole ideological culture behind these kinds of writings which has its own symbology and idioms. So, unfortunately, you have to know or figure out the different relevant pieces of Catholic ideology to be able to parse poetry of this kind.
In the first sentence cuiquam is the agent of flebilis. So, the literal meaning is "That one dies not lamentable to anyone," or more figuratively as we would say in English "He dies not lamented by anyone".
Quem refers to the subject of the previous clause (ille). So, the subject of the previous clause is the object of the next clause (because quem is accusative).
numina refers to the divine powers of heaven in Christian theology
caelus is the sky. Caelus is the ancient personification of the sky. In Christian theology Caelitum is the personified abode of the sky, the "temple of the heavens".
honestas and decor are the subject of sacrarunt. Therefore, it says:
...whom the honesty of life, and the propriety of loyalty, consecrated among the divine powers of the temple of the heavens...
Expertem modifies quem, the subject of the stanza (ille). gravis ambitus is in the genitive and is the classification of Expertem (destitute of...). ambitus literally means something canvassed. To canvas means to walk around and petition people. By extension it means any perimeter. In Christian theology it refers to the "compass of the heavens". In other words, the sun and the planets revolve around the earth, so they constitute the perimeter of the universe. Hence, in theology the ambitus is the cosmos. However, here, the word is being used metaphorically. Erasmus described Satan as auctor ambitus iniqui (the author of sinful pride). So, in other words, Erasmus characterizes Satan as the wonted ambitus---somebody who wants to possess the whole universe. Thus, in Catholic ideology, the term ambitus signifies the cardinal sin of Pride. Hence, altogether the stanza reads literally as follows:
That one dies not lamentable to anyone,
Whom honesty of life, and propriety of loyalty,
Have consecrated among the divine powers of the Temple of the Heavens,
(Who is) Destitute of oppressive pride.
or more figuratively,
He dies not lamented by anyone,
Whom honesty of life, and propriety of loyalty,
Have consecrated among the divine powers of the Temple of the Heavens,
One destitute of oppressive pride.