Loew's First membership is totally free! In exchange for becoming a member you have the right to request an upgrade upon arrival, if available; you also get a welcome gift (bottle of wine, cookies and milk, or a fruit basket), plus a daily newspaper.
I'm not very good at posting URLs; JessicaR or someone else will hopefully see this post and do it!
Since you are leaving soon though, I would recommend that you call their 800 number and sign up over the phone. Sign up is immediate then.
fyi: Some people have said that if you book at a deeply discounted rate (such as Entertainment Card discount) that you won't get the Loew's membership perks. We did while staying at the Portofino, but our rate wasn't rock bottom (just like yours isn't either), so I don't know what matters. Others had no problem even with the Entertainment rate. Anyway, it doesn't hurt to get the memebership and present it upon check-in. I would also call the HRH ahead of time after you get your memebership number and tell that that you are a member.
I can't find the Loew's 800 number either right now! If I find it, I'll come back and post it!