Can I watch "The LEGO Movie 2: The Second Part" without watching the first one?

You should watch The LEGO Movie first.

• First of all, if you're interested in the second part, the first one is also for you. It's hard to describe the best parts without spoilers, so let's just say that when it comes to The LEGO Movie, everything is awesome.
• As the title suggests, the stories are directly connected - in the sense that the second film starts where the first one ended. You could probably follow the story without knowing anything about the past events, since the core concepts are explained, but some aspects of the movie (being intentionally vague here) could be confusing.
• The returning characters are not introduced again. Their personality and relationships were explored in the first film, which means that even if you catch up fast, you'll still miss A LOT of jokes and references.

So if you skip the first one, it's possible that you will be able to enjoy some individual jokes or a song's gonna get stuck inside your head, but you will be missing out on a lot of fun.

(LEGO Batman is worth watching too, but what you learn about Batman from The LEGO Movie should be enough to appreciate The Second part.)

I haven't seen the second film either, but my understanding is that it is a direct sequel to the first. Specifically, it takes place five years later, with Emmett's world being besieged by Lego Duplo aliens. These aliens appear at the end of the first film, and only by watching that film can you fully understand the context of where they came from and why they're attacking.

Without giving too much away, it's also likely that watching the second film first will spoil the big twist towards the end of the first film, especially since that twist is connected to the aliens and their sudden appearance. So yes, I would definitely recommend watching the first LEGO Movie before watching the second one.

I haven't seen the second film, but it's likely there are plenty of references to the first movie, and that you'll enjoy this second one more if you know the characters and understand those callbacks. But I wouldn't expect such knowledge to be a requirement.

Note that the movie also contains a number of characters from the DC Universe, and at least one of them is a return character from The LEGO Batman Movie. Again your enjoyment will likely be higher if you have some understanding of the background of those characters and how they're portrayed in other movies and TV shows etc., but it won't be a necessity.

Why not simply watch the first one? It's a 100 minutes long and can be easily watched via numerous services and is available on DVD/Blu-ray/etc., so it's not like this is a massive hassle.

The first part of Lego does not greatly affect the second, but if you really want, then it is better to watch the first part, as there are characters important for the second film.