This is one of my favorite games from my childhood. If you haven't ever played it, you owe it to yourself to purchase the remastered version [1] and play it through (it's only $3.79). It's incredibly entertaining and witty. I doubt this game will ever get stale. [1]: https://www.gog.com/game/day_of_the_tentacle_remastered
It's not necessary to have played Maniac Mansion beforehand? I'll admit this has been my main hesitation. I remember when Monkey Island III was big in the late 90s, I was hesitant because I hadn't played the two games that came before it. I ended up doing it anyway at the time, but later I would play all three, and the third one really benefits - in my view anyway - from having played the first two ones, even though…
They address this in the linked article (also from personal experience) -- you really don't need any context from Maniac Mansion to thoroughly enjoy DOTT and they are really totally different games in style and substance.