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”.