The Arabic noun "mawsim" calls for a few remarks:

(1) There is another Arabic word for "season" - "fasl" (pl. "fusuul"). "Fasl", however, can also mean "class" (i.e. a group of students).

(2) "Mawsim" is related to "wasama" (he marked), which is derived from the Semitic root w-s-m.

(3) "Mawsim" has two partially overlapping meanings: (1) any of the four main periods of the year, (2) the appropriate season for a voyage, pilgrimage, etc. An example of this second meaning can be found in the title of a famous narrative work by Tayeb Salih, "Mawsim al-hijra ila al-shamaal" (Season of Migration to the North).

(4) Engl. "monsoon" and Fr. "mousson" both come from Arab. "mawsim".

I was wondering what the difference is between lam + present tense to make a past tense negation, and simply ma + past tense?

In general, both means the action didn't happen, however, using lam with present tense verb gives more emphasis to the negation, we call it (jazm). In other words, using lam + present is stronger in negating the verb comparing to using maa + paste tense verb.

Interesting again Desmond. You're a wealth of knowledge on word origins.

Any chance we will ever get a translation of the song in this lesson?

Yes indeed, the words are:
في وقت الصيف حينما يكون الجو حار.. نتسلّى مع الأصدقاء و العائلة و الجار
which is:
In the summer time when the weather is hot...We have fun with friends, family and the neighbours.