If someone works part time and is paid hourly, is it ok to write down a lunch break as part of his or her hours? Especially in the case that someone is only working 4-5 hours a day total, and not a regular 9 hour work day (and therefore can wait until after to eat, or the lunch hour would add a significant portion to the total work hours for that day).
When dealing with monetary issues, the Halacha usually is כמנהג המדינה, i.e. whatever common practice is in that specific location, unless specified otherwise in the worker's contract.
There it says:
ב: מָקוֹם שֶׁנָּהֲגוּ לָזוּן, יָזוּן; לְסַפֵּק בִּגְרוֹגָרוֹת אוֹ בִּתְמָרִים וְכַיּוֹצֵא בָּהֶם, יְסַפֵּק; הַכֹּל כְּמִנְהַג הַמְּדִינָה.
"Whether you have to provide your workers with food depends on local custom."
So whether you are allowed to take a lunch break depends on what local custom is for your type of work and your length and time of work.
Note, that if your work involves preparing food, then there are specific Halachot, irrelevant of local custom, as documented in סימן של"ז - דין אכילת פועל בשעת מלאכה, ממה אוכל או מתי אוכל
That Siman ends with a general Halacha concerning employees:
כ: מֻזְהָר הַפּוֹעֵל שֶׁלֹּא יְבַטֵּל מְעַט כָּאן וּמְעַט כָּאן, אֶלָּא חַיָּב לְדַקְדֵּק עַל עַצְמוֹ בַּזְּמַן, שֶׁהֲרֵי הִקְפִּידוּ עַל בְּרָכָה רְבִיעִית שֶׁל בִּרְכַּת הַמָּזוֹן שֶׁלֹּא יְבָרֵךְ אוֹתָהּ. וְכֵן חַיָּב לַעֲבֹד בְּכָל כֹּחוֹ, שֶׁהֲרֵי יַעֲקֹב הַצַּדִּיק אָמַר: כִּי בְּכָל כֹּחִי עָבַדְתִּי אֶת אֲבִיכֶן, (בְּרֵאשִׁית לא, ו) לְפִיכָךְ, נָטַל שְׂכָרוֹ אַף בָּעוֹלָם הַזֶּה, שֶׁנֶּאֱמַר: וַיִּפְרֹץ הָאִישׁ מְאֹד מְאֹד (בְּרֵאשִׁית ל, מג).
A worker has to be careful not to waste time - even a few minutes here and there; he has to be punctual about his work hours - to the extent that we see that employees are exempt from reciting the 4th Bracha of Birkat HaMazon (so as not to waste time, as it's a Rabbinic enactment).
Similarly, he is expected to work with all his might (physical or mental) as we see that Yaakov Avinu said "I worked for [Lavan] with all my might". He was rewarded even in this world for his dedication, as it says "and he became extremely rich".