Actually, Liberty had more applicants than Harvard (48,936 versus 37,307) in fall 2015. However, it is rather likely that the set of Liberty applicants with academic qualifications like those of Harvard applicants is considerably smaller.
https://nces.ed.gov/collegenavigator/?q=liberty&s=all&id=232557#admsns
https://nces.ed.gov/collegenavigator/?q=harvard&s=all&id=166027#admsns
Harvard is also less expensive than Liberty on a net price basis for middle and lower income students, based on the net price sections of the pages linked above. But Liberty enrolls more middle and lower income students based on the percentage with Pell grants.