Batteries – Lithium Ion Battery Model in LTSpice

It sounds like the question is whether there is some sort of hysteresis in a lithium (ion) battery such that a load this too resistive will not draw current.

In general the answer is no, there is no minimum supply current needed to stabilize the output of a battery. (Switching power supplies do have a minimum current.) Experimentally, a voltmeter across the battery terminals will have a typical input impedance of 10 MΩ, so it would draw only 0.3 µA of current at 4 V.

In terms of the physics, the minimum current you can have is the resistance of the air between the two external terminals in parallel with any internal leakage. The resistivity of an air gap is ~\$10^{16}\$ Ω·m which will also works to out a resistance of ~\$10^{16}\$ Ω between two terminals on a battery, or about 0.4 fA (femtoamperes) at 4 V.

You can do that by using a "Arbitrary Behavioral Voltage or Current Sources" where you can define the arbitrarily define the behavior of you current source. I will not go in to the details of Arbitrary Behavioral Voltage or Current Sources since this is found in the Help of LTSpice

Additionally from http://ltwiki.org/index.php5?title=Undocumented_LTspice You can find the following section:

Resistors Behavioral Resistors Create a behavioral resistor by right-mouse-button clicking on its Value field and edit its value to read: R=. This feature is undocumented, but is considered permissible to use. The expression syntax is the same as for a general behavioral source (see B-sources in Help). The resistance must not go to zero and negative values can lead to convergence problems, so it is advisable to restrict its values to within a meaningful range as per the following Value example: R = limit(1,100k,V(1,2)*I(V1)) ; R stays between 1 ohm and 100k To plot an I-V curve, start by using the differential cursor to plot the voltage across the resistor. First click and hold down the left-mouse-button (red probe icon) on one side of the resistor and then drag and drop the black probe icon on the other side. Finish by dragging the mouse pointer over the x-axis (a ruler icon will appear) and the click the left mouse button to bring up the Horizontal Axis menu. Change the Quantity Plotted from "time" to "I(R1)" (assuming R1 is your behavioral resistor).