Drop at LTC4065L

Please help me provide a meaningful answer to your question by providing a little more info on the 10mA/90mA currents.  I do not see references in the datasheet to 10/90mA currents, but I do see references to 10%/90% of programmed charge current.  Might you be referring to the spec on p. 3 of the datasheet for ΔV_UVCL ?  I apologize if I have misinterpreted your request.

The data sheet  references to 10%/90% of programmed charge current, the Rprog is 2K, which means that the charging current is set to around 100mA, so I came up with the number of 10mA and 90mA.

Our charging current is at 40mA. So the question is with the numbers given for  ΔV_UVCL  : how will it vary for different charging currents? At the minimum it should be related to the RDS on of the series MOSFET as shown in graph Power FET On Resistance vs Temperature on page 5. 

So will a lower charging current allow me to use a VCC of closer to 3.75Volts ?

I think the best you can do is to interpolate the 10% and 90% figures and arrive at a figure for 40mA that way.  Note that the ΔV_UVCL  figure at 10% and 90% are typical, with min and max specified at 25°C.  The typical figures work out to ΔV_UVCL=148mV for a charging current of 40mA.