How does the secondary coil of a transformer affect the primary coil? How is it in case of Step-up and step-down transformer? Does it obey Lenz's law?
Lenz's law is all about maintaining the magnetic field constant. 

Let's assume Lenz's law is wrong in order to justify it for a transformer: -


  So, if a current is taken from a secondary winding it will produce a
  magnetic flux and that flux would be additive with the flux produced by the
  primary and more secondary current would flow which produces more flux and the transformer would eventually destroy itself!


What happens is that the flux in a transformer (ignoring leakage inductance and DC resistance) remains exactly the same irrespective of how much load current is taken. I know this sounds non-intuitive but it is correct.

Maybe consider these following scenarios: -



This is a single turn coil around a core. A small magnetization current flows due to the inductance of the winding (for a power transformer the inductance is quite large because many turns are used). Now, imagine splitting that coil into two parallel coils: -



The magnetization current is shared between the two coils. Next, what if one coil were open circuited: -



You'd get primary and secondary voltages that are in-phase. If you don't believe that consider the repercussions in the second picture above when the two coils are connected. Finally connect a load to the secondary: -



Magnetization current still flows but the load current in the secondary produces a load current in the primary of equal and opposite value i.e. if turns are the same then ampere-turns are opposing leaving only flux produced by the magnetization current.