So... I'm not sure what you're looking for exactly...
But, for the last part, no, not everything has a crystal lattice - lattice's only occur in solids, and maybe some cases of liquids, though I am not sure on that. And even then, not all solids have crystal lattice's if they are amorphous (without a regularly repeating pattern).
I think your overall question was, how do all the major sciences interconnect? And that's an interesting question and it definitely isn't the easiest question - depending on you want to look at it. I'll post something later if I have time. In the simplest sense though, I'll say this.
If you look at a cell, it's made up of molecules and atoms which are governed by the laws of physics. But even though molecules 'obey' the same rules in physics, they are immensely difficult to model with physics and in some cases, fundamentally impossible. So then what do you do? So now there's this field chemistry which develops it's own system for handling these atoms and molecules and that physics wasn't adequate for. Now this new phenomenon comes along, the cell, which is even more complicated and suddenly all the theories we've been developing in chemistry just aren't adequate to handle the enormous complexity that is the cell, life, etc. So now you have this field biology which attempts to create it's own theories for the cell, and life.
And we can keep going, we want to know, for example, how do people interact? They're made up of cells, easy enough, let's just use our biology theories. Except, it turns out human behavior is SO complicated, not even biology theories suffice so now even a new level of theory has to be developed to try and model human behavior - psychology.
Now, this isn't how each field showed up - in this nice linear fashion, but can be used to show a relationship.
Sure, chemistry may be physics, and biology may be chemistry, and so fourth, but each theory has it's limitations in explaining certain phenomenon.
Yes, if you had a big magnifying glass, you could 'see' all the atoms in our bodies (look into metabolic pathways in biochemistry) but that's the problem! We can't! And that's why there are all these different fields and not just a unified theory of existence ( yet
)!
I think I gave a really shoddy explanation there of my perspective lol.