The LW Downld prefs will remember everything. To get them started again, search the topic again & with the sources you find, your downlds should start again with any luck. A manual Search is much better & more effective than 'any' of the other continue functions.
Some hints: A well set-up LW can start to automatically continue its dwnlding after it's settled down perhaps 2 out of 3 times you open LW.
Optimising LW & Maximising Uplds & Dwnlds A (1st post only) & also
Part B which is even better & last & least are
search & dwnld hints. The latter one I've been thinking about re-writing for some time. That's just for playing it safe. eg- I show all speeds & qualities.