A next-generation liquid-scintillator detector will be able to perform high-statistics measurements of the solar neutrino flux. In LENA, solar Be-7 neutrinos are expected to cause 1.7x10^4 electron recoil events per day in a fiducial volume of 35 kilotons. Based on this signal, a search for periodic modulations on sub-percent level can be conducted, surpassing the sensitivity of current detectors by at least a factor of 20. The range of accessible periods reaches from several minutes, corresponding to modulations induced by helioseismic g-modes, to tens of years, allowing to study long-term changes in solar fusion rates.