Hi Kartik, some random thoughts...

This kind of thing works fine for me....

dr = sforceClient.describeSObject("test__c");
alert("name of result = " + dr.name);
alert("describe results = \n" + dr);
var n = new Sforce.Dynabean("test__c");
n.set("Referring_Facility_New_Lookup__c","0013000000B67jF");
alert ("it's set now");

Things to check for:
Are you sure you set the *Name* of the new field to "Referring_Facility_New_Lookup"? Note, the *name* as opposed to the Label. The name is what's used to build the fieldname in the dynabean mapping, your note mentions the Label, but not the Name.

Are you sure you're logging in with the correct username/account and to the correct service? production at www.salesforce.com vs. sandbox at test.salesforce.com. (This is moot if you're not using a sandbox account, or if you're testing it by loading it into the S-control directly and you don't override the serverUrl in your code.)

It's good to see it in the Enterprise WSDL, but it shouldn't matter because the describe should see it. You are doing the describe on the "Lead" object correct? I don't know why you're not seeing it there, I see it in the above example... under the mappings in the dr object.

In your code, (although this shouldn't relate to not seeing it in the describe object), are the values in your Options to the Select element ID's or text? You need to be .set'ing with ID's.

Good luck, Steve Bower.