Morse code translator in Java
My main complaint about your code is that you rebuild the table used for translation for each and every character you are encoding or decoding. This is a major waste of computational power. In addition I've got some other minor comments:


Why the throws SomeException?  – Do you really need these, as you don't explicitly throw them from your code? I'm not entirely sure on common or best practices here, so this might be a moot point, but couldn't these be removed in your code?
Add more space – The density of your code, makes it harder to read. Add a little vertical space here and there, and it will look a lot better. Consider opening your methods with a newline, so that the signature doesn't interfere with the start of the method. 
How to access the ch from the properties – In the properties file, you have an entry for ch. How do get to this one? Or is this at typo?

Also adding space before for loop or if blocks, helps structuring the code within a method. Finally, adding an extra newline so that it is two newlines between methods helps separate the methods.
Most variables are named well – Mostly good naming, but input is kind of vague. I would prefer text in encode() and morseCode in decode(), and avoid the lowerCaseInput. Having a variable name describing what has happened to it, seems a little strange.


Avoiding the getMorseCode() rebuild

You're in a class, and a class can have a constructor. Utilize this to build the needed HashMap. And instead of having a rather costly getKeyByValue() I would advice in this case duplicate the reverse map, as well. (Another option would be to use some external library to implement some bidirectional map, like the BiMap from the Guava library). This would lead to code resembling this untested code:

public class Coder {
  private HashMap &lt;String, String&gt; encodeMap;
  private HashMap &lt;String, String&gt; decodeMap;

  Coder() {
      this("morse_code.properties");
  }

  Coder(String filename) {
    InputStream input = null;
    Properties properties = new Properties();
    try {
      input = Morse.class.getClassLoader().getResourceAsStream(filename);
      if (input == null) {
        System.out.println("Sorry, unable to find " + filename);
        return; // Or throw bad exception... :-)
      }

      encodeMap = new HashMap&lt;&gt;();
      decodeMap = new HashMap&lt;&gt;();

      properties.load(input);

      for (String text : properties.stringPropertyNames()) {
        String morseCode = properties.getProperty(text);
        encodeMap.put(text, morseCode);
        decodeMap.put(morseCode, text);
      }

    // Catch and cleanup, if needed...  
    } catch (IOException ex) {
        ex.printStackTrace();

    } finally{
      if (input!=null) {
        try {
            input.close();
              } catch (IOException e) {
                  e.printStackTrace();
            }
      }
    }
  }


  public final String encode(final String textInput) {

    StringBuilder encoded = new StringBuilder();
    int textLength = textInput.toLowerCase().length();

    for (int i = 0; i &lt; textLength; i++) {
      String lookup = Character.toString(textInput.charAt(i));
      encoded.append(encodeMap.getOrDefault(lookup, " "));
      encoded.append("   ");
    }

    return encoded.toString();
  }


  public final String decode(final String morseInput) {

    StringBuilder decoded = new StringBuilder();

    for (String morseCode : morseInput.toLowerCase().split(" ")) {
      decoded.append(decodeMap.getOrDefault(morseCode, " "));
      decoded.append(" ");
    }
    return decoded.toString();
  }
}


Here I've also renamed the class to Coder, as it seemed kind of strange to use the Encode class to decode stuff... I've also removed some temporary variables to avoid clutter. 

I also added a second constructor allowing for providing a different filename to the constructor. This way you could change the entire functionality of the encode/decode by providing a different properties file.

Code is untested as I don't have access to do the resources thingy using my online java compiler, but you'll get the gist of the idea.

PS! Using the try-with-resources as Vogel612 exemplifies in his answer, is most likely a better, more up to date way to do the properties reading.