reason of ignition lag in SI engine

I am assuming that SI means 'spark ignition'. Combustion is a chemical reaction process. The ignition spark ionizes the air:fuel mixture in the spark gap and the very high temperature creates free radicals which then proceed to oxidize, making still more free radicals,etc. It take a finite amount of time for the small kernel of initial oxidation to grow and propagate. The resulting flame front then sweeps across the combustion chamber, quenching at the cylinder walls when it hits them.

CI engines also have 'ignition delay' for the same reason. It takes time for the first bit of injected fuel to start oxidizing and generate a fire-ball. The difference between SI and CI is: With SI, all the fuel is in the cylinder at the correct fuel:air ratio (1:15 +/-) when the compression stroke begins and thus when ignition starts. The efficiency of combustion is highly dependent on uniformity of the air:fuel mixture. A mixture with too little fuel (lean) will burn more slowly, exhibit more instability and non-uniform burning, and may detonate as the poorly shaped flame front fails to complete its path before the remaining fuel violently explodes from all the combustion heat.

With CI, fuel is introduced after the compression stroke is mostly completed (and air is real hot), and fuel burning proceeds in the spray plume as the fuel is injected. The CI engine operates very 'fuel lean' and with un-throttled intake air. Power output is strictly a function of the fuel amount injected. There is no 'flame front' sweeping across the combustion chamber. The fire-ball is stationary and burns so-long as fuel injection continues. Intensity of the fire-ball depends on the rate of fuel injection.

'Pumping losses' are much lower for a CI engine and part/low load operation is particularly efficient compared to a SI engine because the entire combustion chamber volume is not filled with air:fuel in a uniform 15:1 mixture. At idle/low load, the air: fuel average ratio may be 40:1 or higher in a CI engine, while SI must remain at the 15:1 to burn.