Dear Pipeline:
Usually, cladding means bonding ss over cs by welding, expliosion or co-lamination process. In that cases - also usually - you don´t need to consider the difference betwen both thermal exp. coefficients.
As you tell us in your post, it is understanding as a ss linning acting as a sleeve into a cs pipe. I believe you don´t need to do that. If cs pipe is fabricated by a seamless process, it could be cladded by an explosion process. Then, both materials are acting as just one.
But, indicated pressure an temp. parameters are not too high.
You should conduct an economic evaluation taking into account the cost of the cladd pipes, welding procedures & associated logistics (qualifications and so on) and all final receiving inspection procedures. Then, you should do the same evaluation with just a ss pipe (316, 321, 347 or duplex ss pipe).
You could become surprised for the results of that evaluations.
Pls. still in contact with the forum and tell us what you did finally.
Regards.