As the water is vital and a sensitive thing, I always carry the water, duly ROed and purified with me to my office. Today due to scorching heat and scintilating sun (shine) I took lemonede (lemon juice) with me, but my colleague said that it is harmful, as the plastic bottle, which I carry water in, is of a branded company of distilled water, and he said that these plastic bottles start emitting something poisonous and so should best be avoided or use and throw these after using it once or twice or thrice. The other colleague said that the lemon juice, becomes lethal after some time, and it must be consumed at the earliest.

Are they right? What is the alternative?

There is partial truth to that.

snopes.com: Reuse of Plastic Bottles

Plastic does emit, but under a lot of heat like a microwave or sitting out in the sun for days.
Lemon, like any other food, spoils, and spoiling is hastened with high heat if it's not a food being deliberately cooked. The sun and heat can also start algae growing in your water, which may not even be harmful.
So I wouldn't worry about what they say, but I would keep reading the latest research, which is still mostly inconclusive.
Many cyclists use lightweight metal bottles for plain water, aluminum mostly with a non-volatile liner, or opaque plastic.

Water is vital and sensitive? Plastic bottles emit poisons when reused? Lemon juice becomes lethal over time? Why wouldn't you Google the truth instead of believing in superstition?

Your distant relatives drank from puddles, just like dogs do today. Neither relatives nor dogs died from it. We all drank from the garden hose as kids without ill effect.

It is sad that you choose to look for a boogyman under your bed instead of rejoicing in the knowledge that humans are more healthy today than at any time in history.