Normally not, except in very specific contexts, where you want to stress how hard you work, or some special task you do. ”A munci” says more about some hard work, to do some activity which require physical contribution, when ”a lucra” is more like to have an occupation (https://dexonline.ro/definitie/munci). ”Eu muncesc/lucrez în fabrică” as opposite to ”Eu lucrez la o fabrică de încălțăminte” (I work in a shoes factory), or ”Eu lucrez la calculator” (I am working at the computer). If you say ”Eu muncesc la calculatror” would mean more like you are hard-working to fix it, or repair it, or you want to stress the fact that you are not wasting the time sleeping in front of the computer. etc.
However, in general, you can use them (and their relatives, like ”muncitor-lucrător”, etc) interchangeable in almost all contexts. There are individual and regional preferences for one or the other, or domain-related preferences, or some grammar contraptions where one is not liked, or not existent (ex: ”lucrativ”).
Well, I have a comment about the ”tips” given for this level, but we can not comment there, so this is the first sentence of the chapter and I will comment here: the Romanian „creion” translates only to ”pencil” in English. The English ”crayon” translates to Romanian ”cretă colorată”.
Actually, crayon can translate to creion colorat. Creta colorată should be coloured chalk
The translation option given to me for this sentence was 'The staff are working much' which does not sound complete in British English.
I think this is an older version. Now it is The personnel (staff is good too) works a lot.
Indeed, to my American ear, I would expect, "The staff is working a lot." Perhaps in English, "much" is often qualified, like "not much", "so much", "too much". So, "The staff is working so much [that...]," does not sound awkward.
When Romanians say "personalul" does it refer to one guy or an entire group? If it's one guy "the staff member works a lot" flows much better in English, if it's a collective noun "the staff works a lot" would work better.