Minecraft Language Files Updater
Python 3, 91 77 bytes
-14 Bytes thanks to OMᗺ
I thought that the printout of a Python dictionary would be close enough to JSON to make it a very competitive language for this challenge.  However, the string representation of python dictionaries is different enough from JSON that I had better luck using python's built-in JSON library. I'll bet this can be done more succinctly in JavaScript.
import json
f=lambda x:json.dumps(dict(i.split(&quot;=&quot;)for i in x.split(&quot;\n&quot;)if i))

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Edit:
Bash + Sed, 68 63 bytes
Bug fix thanks to OMᗺ and Night 2
-5 Bytes thanks to OMᗺ
I realized that it might be more byte efficient to directly convert the text to JSON without bundling it in an object, as was my approach for the python solution.  Per byte, sed is the most powerful language for regex replacement that I know of.
echo {`echo &quot;$1&quot;|sed 's/&quot;/\\\&quot;/g;s/\(.*\)=\(.*\)/&quot;\1&quot;:&quot;\2&quot;,/'`}

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Explanation
echo {`                                  #  prints the leading curly brace
       echo &quot;$1&quot;|sed                     # feeds the input into sed
       's/&quot;/\\&quot;/g;                       # replaces &quot; with \&quot;
       s/\(.*\)=\(.*\)/&quot;\1&quot;:&quot;\2&quot;,/'      # surrounds the left and right hand sides of the equals with quotes and joins them with a colon
`}                                       # prints the closing curly brace