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All objects in nature are divided into two classes: massive and massless. Massive objects always move at less than the speed of light, while massless objects always move at the speed of light. Although many of the properties of massive objects pass into massless properties in the limit of infinitesimal mass, these are two completely different classes with very different properties, both physically and mathematically. No matter how much you accelerate a massive particle, it will never become massless, just as a massless particle will never become massive, no matter how much energy you add or take away from it.
Massless particles, such as a photon, do not have the usual concept of proper time: the time that the photon itself would measure if it had a clock. This does not contradict anything, since the clock is massive and, therefore, lies in a different class, they cannot be accelerated to the speed of light so that they fly next to the photon and measure its time. This does not prevent us from having a concept of time ourselves, moreover, the faster an observer moves for us, the slower the course of his time seems to us. At the limit of the speed of light, we will see that time stops for him. But as I have already said, this cannot be done physically, and no massive body can be accelerated to the speed of light.
Therefore, the life we are used to cannot exist at the speed of light. But you can accelerate any living organism to a speed arbitrarily close, but less than light, then everything will be fine.
Objectively speaking, light moves at its own speed, and we live, do not grieve, and do not pay attention to its speed. And in fact-what kind of life with a mass tending to infinity. What kind of musculature do you need to have to carry it back and forth? The bones won't hold up, because their ultimate strength won't change?