What is the lift force per unit span?
The concept of lift force per unit span comes from potential flow theory. It will need some background information to explain what it means, so bear with me.

In the early years of flight, electricity was new and exciting, and it just happened that the equations which could calculate the strength of an electromagnetic field worked equally well when calculating the local flow change effected by a wing. What is the electrical current in a wire became the vorticity in a vortex, and the strength and orientation of the induced magnetic field were equivalent to the induced flow changes. So the vocabulary of electricity was copied over to aerodynamics, just like brain research used vocabulary from computer science when that was a hot topic.

Now we are left with abstract concepts like induced drag or lift per unit span. It would be so much more descriptive to use proper names, but the authors of technical books learned it that way and are much too lazy to explain aerodynamics any better. 

In potential flow theory, you have sources, sinks and vortices. Sources and sinks are used to generate the displacement effect of a physical body moving through air, and vortices are used to explain why wings bend the flow and create lift. In order to calculate the lift force $L$ of a single vortex in two-dimensional flow, the circulation strength $\Gamma$ of the vortex is multiplied by the airspeed $u_{\infty}$ and air density $\rho$. You will find an equation like $L = -\Gamma\cdot u_{\infty}\cdot\rho$ in many treatises about numerical aerodynamics.

To expand that into the third dimension (and, consequently, into reality), you need to add something measured in spanwise direction - but you have already lift, and adding the third dimension would give a moment (lift times distance) where only lift would make sense. Therefore, this two-dimensional lift is now called "lift per unit of span" so there is still space for a third dimension where two-dimensional flow did already produce lift (counter to any sound intuition).

And no, this is never constant over span. In all cases the vorticity is gradually reduced towards the tips, or explained in a better way, the suction force acting on the wing is gradually reduced when you approach the tips because when the wing ends, nothing can prevent the air from flowing from the high-pressure region below to the low-pressure region on the upper surface of the wing.

While the potential flow mentioned above is the mathematical way of looking at aircraft, lift coefficients are the engineer's way of expressing things. From tests it was soon clear that the lift force of a wing scales with the dynamic pressure $q$ of the flow, that is the product of air density and the square of airspeed: $q = \frac{\rho}{2}\cdot v^2$.

The next observation of engineers was that lift also scales with wing area $S$. To make the lifting force independent of wing size and dynamic pressure, they stripped both from the lift (physical unit of Kilopond, Newton or pound-force) so they arrived at a dimensionless figure which they called lift coefficient $c_L$. Doing so made it much easier to compare measurements or scale up known designs for the next, better design. The lift equation now becomes $L = c_L\cdot S\cdot\frac{\rho}{2}\cdot v^2$