lag does not affect cointegration test

 

"Thus in theory you can test for cointegration either between 𝑦1,𝑡$y_{1,t}$ and 𝑦2,𝑡$y_{2,t}$ or 𝑦1,𝑡$y_{1,t}$ and 𝑦2,𝑡−ℎ$y_{2,t-h}$ and the answer should be the same. Empirically the answer may differ, but hopefully you have a large enough sample so that it does not differ in your case."

Reference: 

https://stats.stackexchange.com/questions/285582/cointegration-with-lagged-variables

So, the lag is best analyzed from cross correlation analysis.