What happens is that Lurker fails to open the trash window if no Action cards are in it initially. However, as a workaround, you can open it yourself after the first "stint" of a Reckless Lurker, and then select to gain the Action card you just trashed for the second "stint".
That "don't open the trash if no Action card is in it" behaviour makes sense for a normal (non-Reckless) Lurker. But by the very nature of what Lurker does, this backfires for a Reckless Lurker.