How to simulate this pulse in LTSpice?
You could try something like this:



Where you can use the measured values (overshoot and ripple) to determine the frequency and damping. \$M\$ is the peak overshoot, \$\zeta\$ is the damping.

$$M\approx 1-\frac{\zeta}{0.6}$$
$$\omega_d=\omega_n\sqrt{1-\zeta^2}$$
$$T=\frac{2\pi}{\omega_d}$$

Note that your sampling frequency is not quite enough to precisely determine the parasitic oscillation, so you will have to rely on your "guts", as well. I used the dice to throw some values there, for exemplification. Also, I exaggerated a bit with the very small value for the rise time, compared to the period, but that's up to you to test. Optionally buffer the output if you're not comfortable with that parallel RLC driving whatever it is that comes afterwards.

You could also use a PWL source, as suggested in the comments, but that will onyl give you what you see on the oscilloscope, as oposed to what actually is. If you're fine with that, godspeed.