In that case, look at this design, a 5th order Chebychev low-pass filter, 0.5dB passband ripple, Corner freq = 15 MHz: Just add input and output shunt capacitors to the filter in that blog post.
14.096 MHz fundamental attenuation = 0.2dB
2nd harmonic attenuation = -40dB
3rd harmonic attenuation = -59dB
Since the 2nd harmonic from the Si5351 is already quite low, the output will easily meet the ham transmitter spectral purity requirements. You can also push the cutoff frequency a bit higher and still meet purity specs.
There will be some additional loss, mostly depending on the inductor Q (as with any similar filter).
Here's a link to that filter calculator:
https://rf-tools.com/lc-filter/For several years I was running a 20m WSPR transmitter based on a RPi (just the RPi, the signal was generated by the internal counters). This put out about 10mW and with a filter like my previous post and a simple dipole, was heard from Japan to Alaska to Europe to New Zealand. Here's a link to a ham-club presentation I did about this:
http://wb6cxc.com/wp-content/uploads/2016/03/Ham-Presentation1.pdfBy the way, the Si5351 waveforms shown in that blog you referenced look pretty bad -- they are typically much cleaner squarewaves than shown. I suspect poor layout or measuring technique.