Check through the formation tendency and stabilization/stability of the cation and /or intermediate, the ratio of the kinetic versus thermodynamic stability towards making of the final product.
Dear B. S. Rawat thank you for posting this interesting technical question on RG. According to the literature reference cited below, lauryl dimethyl amine (= N,N-dimethyl dodecyl amine, DDA) can be synthesized by two different synthetic routes. In the first (preferred) process, n-dodecylamine is converted to DDA by an amine methylation reaction using formaldehyde and formic acid. The second synthetic route uses dimethyl sulfate. This procedure is not preferred because of the high toxicity of dimethyl sulfate. In both cases you start from the primary amine, and apparently no secondary amine is formed during these reactions. For more detailed information please have a look the the following article:
Total Synthesis of N,N-Dimethyl Dodecyl Amine-N-Oxide