Here’s what I did:
Download the client.
Start LOTRO.
On that little launcher screen popup thingy, look at the buttons on the very top. Next to “Support” and “EN” (for English, I think) there’s a down arrow button. Click it.
Choose “Options”.
Go to the “General” tab at the top of the options popup.
At the bottom, select “64-bit client (NEW, Beta!)”