Non inverting DC-DC converter that makes fix 4V from a decreasing voltage from 4,2V to 2,8V?
Yes, there's several ways to do this.


Use a buck-boost converter


This kind of device adapts based on the ratio between input and output voltage. They have three modes: Buck, LDO and Boost. Since your max LiPo voltage is 4.2V or so, the converter would be in LDO mode, then Boost mode as the battery drains.


Use a boost followed by LDO


Before there were buck-boost solutions out there, this is the way it was done. If you could boost up to say 4.5V then regulate to 4V, the losses at 1.5A would be 750mW max. Not ideal.


Use boost, followed by buck


Boost up to 5V, then regulate to 4V using a second buck DCDC. Conveniently, there are lots of solutions for the first part that are specific to USB.

Happy hunting...