Investigating the mechanism of positron annihilation in liquid-scintillator based neutrino experiments could be helpful for positron reconstruction algorithms and positron-electron discrimination analysis. Based on this, we utilize a novel positron annihilation lifetime spectrometer to characterize a series of liquid scintillator samples without direct contact with the positron source by applying the anti-coincidence method, which facilitates the measurement of liquids with high accuracy and low background. We obtain an ortho-positronium (o-Ps) lifetime value of 3.02 ns for liquid scintillators composed of linear alkylbenzene and two solutes, and we also measure liquid scintillator samples by bubbling different gases to study the interaction of oxygen dissolved with positronium. The discussion of the annihilation behavior of o-Ps in liquid scintillators further clarify the factors affecting the lifetime and intensity of o-Ps, and the calculation of annihilation rate and free volume radius within the samples has potential applications in characterizing gas solubility and free volume in liquids with o-Ps as probe.