Slightly late reply but I had the same question. Looks like they are different programs although hotels may participate in both. Room rate appears to be the same for both programs but the Chase LHRC program gives better benefits (ex $100 food credit instead of $25 for the exact same hotel). LHRC benefits seem close to\often the same as Amex's FHR program but will occasionally be different\worse. (Ex FHR is giving a $100 food and beverage credit while LHRC is giving 'afternoon tea for 2' for the exact same property. Cost of afternoon tea for two is $65). Room rates between the FHR and LHRC appear the same from my small number of samples. There do seem to be a few hotels that participate in one vs the other but, largely, they seem to be the same hotels in both LHRC and FHR