What I do is put the frozen roast in a bowl of cold water with a circulating pump ( I use a cheap aquarium pump that I bought for my home made sous vide thingy). It will defrost a pretty solid chunk of meat in surprisingly short time.
I learned about this method from an Alton Brown episode of Good Eats.
Quite ignoring whether it’s dangerous to leave it out, I’m dubious it will thaw in a day at room temp. Definitely submerge it in water, and circulate if possible.
An aluminum baking sheet makes stuff thaw far faster that some might guess. The metal is cold to the touch within minutes. It will also help catch condensation drippings.
Thanks to conductive reciprocity, they also help the other way: hot stock pots, cast iron ovens, other flat bottomed dishes cool or chill way faster with a big aluminum sail underneath. Keep the bottom a little wet for faster chilling.
This might be a rather decadent solution (or perhaps no solution at all) but when faced with this problem, I sometimes just go and buy another leg of lamb (fresh, unfrozen) and use that, then save the frozen one for another occasion where thawing can be planned in time.
Well it’s late, but the fastest method that I have found in such a must do situation is hot water at first till the outer parts thaw a bit, then luke warm water till done (or start cooking). The outer surface will get cooked/crusted anyway so a little precooking doesn’t make much of a difference in the end product.
Also I have tried the microwave, but the hot water method is both faster and doesn’t make weird very hot over cooked areas.
Again, probably too late, but my advice is pretty much identical to @Tatterdemalion, with a touch more nuance.
If I’m doing large scale cooking, I’m often short on refrigerator and sink space. So, when I’ve needed to do a speedthaw before, I put the frozen food inside a large coleman cooler I had already, filled it with water, and ran my spare aquarium pump (actually the spare to be used for water circulation in my cat fountain) inside, and left it in my garage or on the catio depending on the time of year. You WILL of course need to leave the top off, or, well, the insulation works against you, to no one’s surprise.
With the meat fully submerged, I figure a 4ish hours with the pump running starting with cool but not cold water, but results very depending on how much meat and how bit the cooler is.
Again, just leaves a lot more space to work on everything else in the kitchen.
I always thawed turkey, chicken, and other frozen meat that is well wrapped (cryovacced) in a bucket of cold water, in the basement deep sink or the bathtub. With a trickle of cold water running into the bucket. I went down every hour and refreshed the water in the bucket.
I must strongly advise to make sure the drain is not blocked!
Not intentional. I accidentally used the French term from the packaging. I sometimes mix things up a bit between English and French; it didn’t say “Lamb jigot” but in my hurry to get it thawed, “Lamb roast” and “Jigot d’agneau” got franglaised.