do you consider a lattice point to be a point {x,y} where x,y are integers? Lattices can be however you define them.

If so

how often will an x value produce an integer y value given the denominator of both terms in y(x)?

How many integer values of x are there for {-100 <= x <= 100}

So roughly how many lattice points will there be?

Now look at the edges of your x domain and make sure you don't have to subtract 1.

-4(-98)+70 = 462 which is divisible by 3, so they start at -98

-4(100)+70 = -330 which is divisible by 3 so they stop at 100

You can figure out how many there are from all this.