1-5 dicarboxylic acid to lactone with SOCl2?
The simplest 1,5-dicarboxylic acid is glutaric acid (pentanedioic acid in a more systematical naming). If you react it with $\ce{SOCl2}$, you will indeed intermediately arrive at a compound that has one carboxylic group and one acid chloride group. Then, as you suggest, the other carboxylic acid can attack the acid chloride and $\ce{HCl}$ is eleminated.

However, the resulting product is not a lactone but rather glutaric anhydride; a cyclic acid anhydride. To convert it to a lactone you would need to remove exactly one carbonyl group. Whether this is done before or after the reaction with $\ce{SOCl2}$ does not matter, but before sounds easier to me.