conjugating first "let's" in "special we imperative" but not for second "let's".

Hola Mary

I'm not sure which exact word you saw for your second example? but I imagine you saw "disfrutemos" as the imperative/present subjunctive of disfrutar (let's enjoy ourselves)

If this is what you saw, disfrutemos doesn't have the reflexive pronoun "nos" in it because we don't use it as reflexive (despite saying in English let's enjoy ourselves. 

So, in the first one: olvidémonos 

you have olvidemos (imperative/present subjunctive) + nos (the reflexive pronoun because in this case we are using the verbal structure "olvidarse de algo" and this requires the reflexive pronoun. 

In the second one: disfrutemos

you just have the verb disfrutar conjugated in the imperative/present subjunctive with no pronoun, so here you don't need to drop the -s from the ending -emos. It's only when you have the ending -mos followed by the pronoun nos when you drop the previous -s.

I hope this clarified it.

Saludos cordiales

Inma