Yes, there is a small amount of time dilation expected in the L1 Lagrange point between the Earth and the Sun, although the effect is relatively minor. The L1 point is a point of gravitational equilibrium where the gravitational pull of the Earth and the Sun balance each other out, allowing objects to remain relatively stationary with respect to the Earth-Sun system.
According to the theory of relativity, gravitational fields can cause time dilation. In the case of the L1 point, the gravitational fields of the Earth and the Sun combine, creating a region where time runs slightly slower compared to a location farther away from these massive bodies. This means that clocks in the vicinity of the L1 point would experience a slightly slower passage of time compared to clocks farther away from that region.
However, the time dilation effects at the L1 point are extremely small and practically negligible for most purposes. The difference in gravitational potential between the L1 point and Earth's surface is relatively small, resulting in only a tiny time dilation effect. To put it in perspective, the time dilation at the L1 point is estimated to be on the order of microseconds over the course of a year.
So while time dilation does exist at the L1 Lagrange point, its effects are so minuscule that they are not practically significant in most scenarios.