How are lightning and thunderstorm intensity linked?
Is the ratio of IC to CG lightning relevant?

Yes. Primarily, severe storms tend to have very few cloud-to-ground (CG) strikes. Thus, the ratio of IC:CG is likely going to be very high.1 2 However, some severe storms do produce a significant amount of positive CG strikes. They would still have a high IC:CG ratio, but they would distinguish themselves by having more positive CG strikes. However, both of these types -- low-CG and some-positive-CG -- are potentially severe.2
It is important to note that the amount of CG strikes can be dependent both on where in the lifecycle a storm is, and the physical location of a storm (CG characteristics appear to be region-dependent). In tornadic supercells, the total amount of lightning seems to decrease during tornadogenesis, and the CG rate appears to increase after the tornadic stage of that supercell ends.3
There doesn't appear to be any existing literature on amplitude as a measure of severity. Perhaps, through this work, you might be able to identify whether this is an area which should be studied further.
References
1 Donald R. MacGorman, Donald W. Burgess, Vladislav Mazur, W. David Rust, William L. Taylor, and Brenda C. Johnson, 1989: Lightning Rates Relative to Tornadic Storm Evolution on 22 May 1981. J. Atmos. Sci., 46, 221–251, doi: 10.1175/1520-0469(1989)046&lt;0221:LRRTTS&gt;2.0.CO;2.
2 Timothy J. Lang and Steven A. Rutledge, 2002: Relationships between Convective Storm Kinematics, Precipitation, and Lightning. Mon. Wea. Rev., 130, 2492–2506, doi: 10.1175/1520-0493(2002)130&lt;2492:RBCSKP&gt;2.0.CO;2.
3 Scott M. Steiger, Richard E. Orville, and Lawrence D. Carey, 2007: Total Lightning Signatures of Thunderstorm Intensity over North Texas. Part I: Supercells. Mon. Wea. Rev., 135, 3281–3302, doi: 10.1175/MWR3472.1.
Further Reading

Lawrence D. Carey, Steven A. Rutledge, and Walter A. Petersen, 2003: The Relationship between Severe Storm Reports and Cloud-to-Ground Lightning Polarity in the Contiguous United States from 1989 to 1998. Mon. Wea. Rev., 131, 1211–1228, doi: 10.1175/1520-0493(2003)131&lt;1211:TRBSSR&gt;2.0.CO;2.

Yeung, Linus HY, E. S. T. Lai, and S. K. S. Chiu. &quot;Lightning Initiation and Intensity Nowcasting Based on Isothermal Radar Reflectivity-A Conceptual Model.&quot; The 33rd International Conference on Radar Meteorology. 2007.

C. Emersic, P. L. Heinselman, D. R. MacGorman, and E. C. Bruning, 2011: Lightning Activity in a Hail-Producing Storm Observed with Phased-Array Radar. Mon. Wea. Rev., 139, 1809–1825, doi: 10.1175/2010MWR3574.1.