This study investigates the characteristics of oscillating lifted flames in laminar coflow-jets experimentally and numerically by varying both fuel density (by varying propane and n-butane mixtures) and coflow density (by diluting air with N2/He mixtures). Two different lifted flame oscillation behaviors are observed depending on these parameters: oscillating tribrachial lifted flame (OTLF) and oscillating mode-change lifted flame (OMLF), where a rapid increase in flame radius is observed. The regimes of the two flames are identified from experiments, which shows that OMLF occurs only when the effect of the negative buoyancy on the flow field by the fuel heavier than air becomes significant at low fuel jet velocity. OMLFs are also identified to distinguish OTLF regime from flame extinction, which implies that an OMLF can be extinguished when the positive buoyancy becomes weak, losing its stabilizing effect, or when the negative buoyancy becomes strong, further enhancing its destabilizing effect. Transient numerical simulations of both OTLF and OMLF reveal that the OMLF occurs by a strong toroidal vortex and a subsequent counterflow-like structure induced by relatively-strong negative buoyancy. Such a drastic flow redirection significantly changes the fuel concentration gradient such that the OMLF changes its mode from a tribrachial flame mode (decreasing edge speed with fuel concentration gradient) to the premixed flame-like transition mode when the fuel concentration gradient becomes very small (increasing edge speed with fuel concentration gradient). Again, a tribrachial flame mode is recovered during a rising period of flame edge and repeats an oscillation cycle.