The Josephson diode effect (JDE) has attracted a lot of recent attention for its potential application in superconducting circuits as a logic element. However, it can also serve as a potent tool in probing the spin-momentum locking and time-reversal symmetry breaking in the superconducting state. In this work, we establish the presence of a large JDE in a van der Waals transition metal dichalcogenide and type-II Dirac semimetal 1T-PtTe₂ and distinguish between intrinsic and extrinsic mechanisms contributing to the effect in lateral Josephson junctions (JJs). A large second-harmonic component in the Josephson supercurrent is shown to exist through analysis of the current-phase relationship that also serves as an essential ingredient for the existence of an intrinsic JDE, thus making it also a useful probe of second-order Josephson supercurrents in a junction. We refer to junctions with such current-phase relationships as ‘second order φ₀- junctions’, discuss their properties, and differentiate them in terms of the diode effect from junctions with other well-known current-phase relationships. The presence of a large second harmonic component in PtTe₂ JJs is attributed to the long-range phase-coherent transport facilitated by the Dirac-like spin-momentum locking in the system. The high chemical stability, high transparency, and large spin-orbit coupling along with large critical currents provided by PtTe₂, make it an interesting platform to further investigate the Josephson diode effect.