Uhhhhhhhhhhhhhhhhhhhh NO.
The trick behind this is that it appeals to your senses (and it shouldn't be hot... simply luke warm at best)... people crave certain smells that appeal to them. If you love soda when you smell one you'll want it.... lemon water has that effect on your senses, it curbs the craving of wanting the sugary sweet drink like soda or whatever.... and still getting in water. The point is to drink water over "empty calories" and in turn you're drinking your daily supply of water. This alone allows you to lose weight because you're decreasing your calorie intake and increasing your fluid intake which is good for your metabolism but the actual "water" and "lemon" as ingredients to help lose fat faster is a big FALSEHOOD and your colleague is a bone head
The luke warm vs. the extreme hot or cold allows you to drink MORE water. Room temperature water can be consumed in larger quantities without satisfying your thirst as quickly, burning your mouth or giving you brain freeze.