The park lies in the center of the town.

[diamondcutter]

We can say:
The town lies in a small wooded valley.
Germany lies in Europe.

I’d like to know if it’s natural to say these sentences:
The park lies in the center of the town.
Our school lies to the east of the park.
The hotel lies in the west of the city.

 

[jutfrank]

The Germany example is no good. It would be far better if you were to add a more precise location.

The others are okay.

 

[Tarheel]

I would use "is" in all of your examples.

 

[diamondcutter]

I'd like to know whether the verb "lie" is a big word or too formal for the small places like a school, a hotel and a park in the contexts in the OP.

 

[WilliamC340]

We can say:
The town lies in a small wooded valley.
Germany lies in Europe.

I’d like to know if it’s natural to say these sentences:
The park lies in the center of the town.
Our school lies to the east of the park.
The hotel lies in the west of the city.

They're fine.

I am not a teacher.

 

[tedmc]

I wouldn't use "lie/lies" with a place. "To lie" is to have something rest flat in a horizontal position.
I would use "located", since you are talking about where the place is.

 

[Peedeebee]

Lies is a perfectly good English idiom to describe the location, geographically, of a place such as a village, a school, a hotel, a park. It's fine with the concept of lying horizontally. It perhaps implies a spread-out location. Maybe you wouldn't say it of a TV tower or a well, or a mural, or of a plaque that a tourist wanted to see, but of something covering more area.
You probably wouldn't use it for Germany. Describing Germany as in Europe, is part of Germany's identity, and of Europe's identity. It's also fairly well-known. The idiom is more likely to be used to decribe a place which is unfamiliar to the listener. Also, if you wanted to say... that's why the (park) gets wetter weather than the (town), then lies would seem even more suitable, as you are comparing the locality of one place to another.

 

[tedmc]

Shouldn't "Lies" be in inverted commas? Yes, I would use it for a sprawling geographical feature.