From London it takes about 45mins on the high speed train from St Pancras Intl or Stratford Intl to Gillingham. You can also catch a slower train from Victoria or Charing Cross. It takes about 25mins to walk from the station to the Lightship.
For other travel details see http://www.lv21.co.uk/contact-us/
There is free parking adjacent to the Lightship.