I hunted there last year and really enjoyed it. After hunting for my buff up at Chirisa, we drove down to hunt at Lemco for 8 days. The place is huge (950,000 acreas at last count--it used to be 1 million, but the land grab cost them a parcel). You'll have a chance at a remarkable assortment of game when there. The one issue you'll need to investigate is that the place is divided into different sections and each has its own quota of animals. When there, one of the things I really wanted was a sable. The section where I hunted had very few, while another section that had used up its quota by the time that I got there had plenty. You'll want to check with your safari company (probably HHK), to make sure that you'll have the best chance for the species you want.
As for the best time to go, they'll tell you that you will more easily find game in Africa when it is dry as the animals congregate near water, making them easier to hunt. That is definitly true, but the driest part of the year is in Sept/Oct, which also happens to be getting late in their hunting season, which could create situations like I found with my sable. The point is that you need to communicate with your outfitter and let them know what you want before you go and where you have priorities. No doubt they'll make every effort to meet your requests.
The accomodations there are awesome. They really do treat you well. Here are some pics from Lemco:

Here's where I ate each morning and evening (sometimes inside, sometimes out)

My room while there:

The view from my room (we were up on a hill):

A few giraffes...I chose not to shoot one (no challenge):

Here's what you do (sleep) after spooking eland at Lemco before resuming your pursuit...

Here's the eland I eventually shot. It scored 101 5/8 with its 38 3/8" horns.

Here's the rest of the stuff I shot while at Lemco. My buff isn't pictured as it was shot, as I mentioned, at Chirisa the week before.

And if you need a bit of refreshing in the evening, your Lemco lodge will have something like this:

Good luck!