In my attempts to locate a lucky egg, I learned of a strategy consisting of a yanma with compound eyes ability, a banette with frisk ability, and a mr.mime with the move trick.
Faint the yanma but leave it at the front of the party so it's compound eyes ability still works to get 50% of the wild encounters have items. This way banette goes out and frisks them, and if I don't want the item, I can run. If I want it, I can switch out mr.mime and use trick to obtain it. Last night doing this, I found a chansey in the trophy garden and saw it had a lucky egg, so I used trick and got one.
EDIT:And while looking for gengar in the old chateau, I found a shiny ghastly!