Okay think about what you just told me. You told me something with NO CHARGE is lipophilic.
In this instance, we think of it has having no charge. Ignore this non-polar business. That just means it won't dissolve in water. That's why it's drawn to the fats; imagine dropping a whole drop of oil in some water, it would sit together and not separate out into the water. When you only have one particle it sits together in the water regardless of its polarity, unless that particle is polar and made up of several atmos with different polarities. So basically, the particle won't separate out into different atoms when you place it in water. It has no charge because of this.
Ergo, it won't be repelled by the hydrophilic head, because it has no charge. It just LOVES LIPIDS, hence the name, so it can be drawn through the layer and out the other side presumably by standard diffusion.
So let's break it down a little more easily.
A hydrophilic head and a hydrophobic tail are repelled by or attracted to water (not each other!)
So when the particle approaches the hydrophilic head, the particle clearly isn't water and it isn't dissolved in water. It has no charge so it can't be repelled by the polar head.
It has no charge so it won't be affected by the head or the tail. Therefore, the hydrophilic head won't repel the particle and neither will the hydrophobic tail. In fact, the hydrophobic tail is the same polarity as the particle, just as the hydrophilic head is the same polarity as water. Therefore, the particle is considered lipophilic as it loves the lipid of the membrane just as the hydrophilic head loves the water in the surrounding fluid. The fact that it passes through the head is irrelevant; the head is still a lipid, and it'll let the particle pass through because the particle has no charge. The head can't repel something with no charge.
My explanation skills when it comes to biology are now a little rusty but for the purposes of this question I hope I have sorted out any possible flaw you can see in the theory.