Is this how the lowpass butterworth analog filter can be implemented?
Yes but there are a lot of details; like merging R4 with a termination impedance and using pre-distortion to compensate for finite Q in the inductors.  I would suggest reading some wikipedia articles:
https://en.wikipedia.org/wiki/Analogue_filter
https://en.wikipedia.org/wiki/Network_synthesis_filters
https://en.wikipedia.org/wiki/Butterworth_filter
https://en.wikipedia.org/wiki/Electronic_filter_topology#Ladder_topologies
To get a feel for you want.
Then you can decide how far you want to go along this path.  Whether to learn how to do it yourself or find some prepacked program.  But, unless you  feel lucky today, proceed with caution and some knowledge.  There are a lot of in's and out's; pitfalls. 
I have always found the field fascinating; but that's partially because it is complicated and fundamentally mathematical :)  Your mileage will vary.
BTW: this is a DSP forum not an analogue design forum.