"":35j6qym4]I am aware that the letter V is used in place of U and pronounced as W in most cases."
To be more precise: There is no "Vee" in Latin at all. There is a letter that LOOKS like the English 'V' but is actually the shape of the Latin 'U,' which, as a consonant, is the same as the English 'W.'
"This explains the omission of letters U and W from the LQS."
It's because they don't exist in the Latin alphabet (see above for clarification).
"I'm assuming that any hard K sounds will be given the value of the letter C?"
There is no K in Latin. There are Latin words with K in them, when this came from another language. - So, if you're only using this for Latin words, by "hard K sounds" do you actually mean the letter K?
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There is no J in Latin. It is the letter I. However, when acting as a consonant, some post-Latin writers of Latin have substitute a 'J' shape for the letter. When the I is a consonant, it is pronounced like our Y.
Your Deus Meumque Jus would actually be written, in Latin characters, as DEVS MEVMQVE IVS (since the Latin 'U' is written to look like 'V,' and there is no J in Latin).
"Does one simply ignore the letter (like vowels in Hebrew) or should one give the value of the closest equivalent?"
One should determine what the Latin letter actually is/was, and use that. No need for "closest equivalent." It's just that a lot of people writing Latin in recent centuries have tried to make it easier for themselves by substituting more familiar letters where convenient.