For this to work ,I think your custom routes should come above dafault route. i.e DefaultApi2 and DefaultApi3 should come above DefaultApi1.
Also to be RESTfull you can also try avoiding extra default routes and use only default route 1 and do HttpGet
to /api/LVChart
, like this
.../api/LVChart?lines[]=15&lines[]=11&lines[]=12&lines[]=3&lines[]=10&lines[]=7&swapAxis=false