The integrated sensing and communication (ISAC) systems based on the linear frequency modulation (LFM) waveforms have attracted substantial attention. However, existing routines suffer from additional synchronization preamble overhead, which limits both communication and sensing performance. This work, using the dual-chirp with opposite slopes, exploits a preamble-free synchronization scheme for the LFM-based ISAC. We first theoretically analyze the quasi-orthogonal property of the proposed dual-chirp LFM waveform and derive its achievable communication rate and range ambiguity function. A photonics-assisted proof-of-concept ISAC experiment is conducted in the 300 GHz frequency band, achieving a 20 Gbps data rate with a distinguished peak sidelobe ratio (PSLR) of up to 29.2 dB and 1.5 cm range resolution. More importantly, less than 0.5% synchronous power overhead is needed in our scheme. In addition, the performance trade-off induced by the data rate and amplitude ratio is validated in the experiment, which is in line with our theoretical analysis. Therefore, the proposed scheme provides a promising solution for synchronizing LFM-based future ISAC systems.