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HTML

<script src="https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min.js"></script>

JavaScript

var array = [
  {
    "F": "cis-1,2-Dichloroethene:MW-002",
    "Chemical": "cis-1,2-Dichloroethene",
    "LocName": "MW-002"
  },
  {
    "F": "Tetrachloroethene:MW-004",
    "Chemical": "Tetrachloroethene",
    "LocName": "MW-004"
  },
  {
     "F": "Tetrachloroethene:MW-003",
     "Chemical": "Tetrachloroethene",
    "LocName": "MW-003"
  },
  {
     "F": "Tetrachloroethene:MW-002",
     "Chemical": "Tetrachloroethene",
    "LocName": "MW-002"
  },
  {
    "F": "cis-1,2-Dichloroethene:MW-001",
    "Chemical": "cis-1,2-Dichloroethene",
    "LocName": "MW-001"
  },
  {
    "F": "Tetrachloroethene:MW-001",
    "Chemical": "Tetrachloroethene",
    "LocName": "MW-001"
  },
  {
    "F": "cis-1,2-Dichloroethene:MW-004",
    "Chemical": "cis-1,2-Dichloroethene",
    "LocName": "MW-004"
  },
  {
     "F": "cis-1,2-Dichloroethene:MW-003",
    "Chemical": "cis-1,2-Dichloroethene",
    "LocName": "MW-003"
  }
]


var temp = _.sortBy(array, ['Chemical', 'LocName']);

console.log(temp)