  Gravitational lensing can happen not only for null signal but also timelike
signals such as neutrinos and massive gravitational waves in some theories
beyond GR. In this work we study the time delay between different relativistic
images formed by signals with arbitrary asymptotic velocity $v$ in general
static and spherically symmetric spacetimes. A perturbative method is used to
calculate the total travel time in the strong field limit, which is found to be
in quasi-series of the small parameter $a=1-b_c/b$ where $b$ is the impact
parameter and $b_c$ is its critical value. The coefficients of the series are
completely fixed by the behaviour of the metric functions near the particle
sphere $r_c$ and only the first term of the series contains a weak logarithmic
divergence. The time delay $\Delta t_{n,m}$ to the leading non-trivial order
was shown to equal the particle sphere circumference divided by the local
signal velocity and multiplied by the winding number and the redshift factor.
By assuming the Sgr A* supermassive black hole is a Hayward one, we were able
to validate the quasi-series form of the total time, and reveal the effects of
the spacetime parameter $l$, the signal velocity $v$ and the source/detector
coordinate difference $\Delta\phi_{sd}$ on the time delay. It is found that as
$l$ increase from 0 to its critical value $l_c$, both $r_c$ and $\Delta
t_{n,m}$ decrease. The variation of $\Delta t_{n+1,n}$ for $l$ from 0 to $l_c$
can be as large as $7.2\times 10^1$ [s], whose measurement then can be used to
constrain the value of $l$. While for ultra-relativistic neutrino or
gravitational wave, the variation of $\Delta t_{n,m}$ is too small to be
resolved. The dependence of $\Delta t_{n,-n}$ on $\Delta \phi_{sd}$ shows that
to temporally resolve the two sequences of images from opposite sides of the
lens, $|\Delta \phi_{sd}-\pi|$ has to be larger than certain value.
