what is lumped parameter method for analysis
It is a type of finite element analysis.
Instead of performing the differential equations to determine the response of a structure, you assign stepwise regions where the parameters are constant (EI, GJ, mass per length, etc.) and use influence coefficients to determine how each section affects the other sections.
Lumped parameter methods can be applied to finite difference as well, e.g.
Heat Transfer and Fluid Flow Design and Analysis Software
Basically as enigma indicated, it is a method to simplify the solution to a rather complex system.
For example, one would model an entire nuclear reactor based on the thermal energy generated by the entire core, say 3500 MW. However in the reator, there are 193 assemblies in which power generation is spatially dependent. A lumped parameter model would ignore the spatial dependence. Within the core, one simply uses an average (or global heat transfer coefficient).
This approach can be used to linearize a non-linear problem.
In electronics, the use of equivalent circuits would be considered a lumped parameter model - http://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.html, or http://hyperphysics.phy-astr.gsu.edu/hbase/electric/norton.html#c1.
Separate names with a comma.