We are in the process of remediation, re-engineering old JS web resources for latest D365 v9 sdk changes w.r.t Client scripting API improvements & deprecation.
W
I just tried in v9.1.0.3832 var data = { _[LookupFieldName]_value : null } is working for me.
var data = { _[LookupFieldName]_value : null }
var data = { "statecode": 1, "*_myprefix_mylookupfieldname_value*": null } Xrm.WebApi.updateRecord("*entityName*", *recordId*, data);