Interior door locked, key not provided

Our toddler locked an interior door, so we can't get into our bedroom. We contacted the landlord for the key, to which they responded they didn't have one, and they provided us with contact info for a locksmith. When asked who would cover the cost ($100), they responded that they didn't lock the door so it's on us. I disagree since they should be providing keys. I'm in Indiana. Nothing is specified in the lease regarding this. Do I have any relief here?

Edit: To answer some of the common questions:

No it's not a normal interior handle with just the small hole with the button, it's a standard exterior type handle that requires an actual key.

No my toddler was not trapped inside.

I can't take the door off, because the hinges are on the other side.

I can't remove the handle, because the screw access holes are also on the other side.

I was able to get it open by using an old credit card, thankfully, so don't need a locksmith.

The landlord did offer to replace the door handle with a normal interior doorknob.