I'm afraid as asked this is very difficult to answer.

The reason is that in the 1930's most street lighting was provided by a City; City Borough; Municipal Borough; Urban District Council ; or Rural District Council (http://www.simoncornwell.com/lighting/timeline/ page down to '1875') and there were a large number of those within Lancashire.

Even today, after many reorganisations which tended to reduce the number of councils, there are 19 councils within Lancashire (http://www.information-britain.co.uk/detail.cfm?county=19&EstType=22). In the 1930's there were many more.

Each of these councils were able to make independent decisions about how to colour lamp posts.

There is some information here - http://www.grewelthorpe.org.uk/History/street-lights - about the small size of administration at which street lighting decisions where made in the early years of the 20th Century. That's about a place in what is now North Yorkshire rather than Lancashire but I think it does illustrate the small scale at which these things were done and hence the potential for many different decisions to be made.

If you're interested in a particular town rather than the whole of Lancashire you might have more luck talking to the local historians for a given Council area and seeing if they have any colour pictures of the time.