LSE EMFSS International Programme is taught and assessed by LSE, almost all Modules, Courses, their content, and programme structure are the same like the ones taught on-campus, your application is reviewed and approved by LSE panel, you can switch from online to on-campus anytime during the first 2 years.
Note in the past LSE did not have right to award degrees and diplomas, so at that time LSE students used to be enrolled as "external" students at UoL and were awarded the degree from UoL after completing their studies at LSE.
so for me a graduate can safely and confidently say "I studied at LSE and my degree was awarded by UoL", nobody will think you are fraud!
It's here more political and economical than anything else, because you pay less fees.
However it's different story when you study online BSc Business Administration (direction from Royal Holloway) via Coursera, as it seems to me that the assessments are not done by Royal Holloway. But I here believe UoL reputation outweighs Royal Holloway.