What is the colourless gas having suffocating smell dissolves in lime water?

The answer is Carbon Dioxide (CO2).

I assume this is what you mean - Carbon Dioxide is the waste product of respiration that can suffocate some animals, including humans. It is used by plants in photosynthesis, and these plants produce Oxygen (O2). It reacts with lime water and turns it a sort of milky colour.

The equation for this reaction is

Carbon Dioxide (CO2) + Calcium Hydroxide (Ca(OH)2) ---> Calcium Carbonate (CaCO3) + Water (H2O)