Lithium ion battery cutoff current?
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.