Edit in JSFiddle

const object = {
  a: 1,
  b: {
    b1: 1,
    b2: 'a',
    b3: null,
    b4: undefined,
    b5: {
      b51: 1,
      b52: 'a',
      b53: null,
      b54: undefined,
      b55: ''
    }
  },
  c: ''
};

const expect = {
  a: 1,
  b: {
    b1: 1,
    b2: 'a',
    b5: {
      b51: 1,
      b52: 'a'
    }
  }
};


function removeObjectBy(object, condition) {
  // lodash#cloneDeep
  const _obj = _.cloneDeep(object);
  
  const _cond = typeof condition === 'function' ? condition : function () {};

  function _remove (obj) {
    for (let o in obj) {
      if (typeof obj[o] === 'object') {
        _remove(obj[o]);
      }
      if (_cond(obj[o])) {
        delete obj[o];
      }
    }
  }

  _remove(_obj, _cond);
  return _obj;
}

const isEmpty = val => val === '' || val === null || val === undefined;
const actual = removeObjectBy(object, isEmpty);

document.getElementById('origin').innerText = JSON.stringify(object, null, 2);
document.getElementById('expect').innerText = JSON.stringify(expect, null, 2);
document.getElementById('result').innerText = JSON.stringify(actual, null, 2);

<pre id="origin"></pre>
<pre id="expect"></pre>
<pre id="result"></pre>