(1) You can't use lowess as it is a data exploration tool. The degree of flexibility of the function is set by the user. So if you play around with the function you'll see that you get dramatically different results depending on the bandwidth you select. (in R this is "f" the smoother span)
(2) There are a number of smoothing functions that derive the degree of flexibility from the data rather than being set by the user. As a result they can be used in this situation. These include restricted splines, GAM, and MARS (in the Earth package). But there are many more. I prefer GAM and MARS and would use MARS in this situation, or GAM if I was planning on publishing. Restricted splines are likely the most accepted/commonly seen method.
(3) You can sometimes just show that the smoothing functions look different:
"Relationship Between Hospital Readmission and Mortality Rates for Patients Hospitalized With Acute Myocardial Infarction, Heart Failure, or Pneumonia" JAMA
In the case of MARS this is dramatic and might be sufficient.
(4) You do have a sparse data issue. In the flexibility of the functions above are derived from the data having more data might be better (give you less biased estimates).
(5) You could avoid all this, but I don't think it will be that popular, doing something like: creating a 5 level categorical variable from chromosome size "size_cat"
regress fold ~ size size_cat
in the first graph both size and size_cat will be non-significant. In second graph both will be significant. And you could say size=captures linear relationship size_cat non-linear relationship
Maybe not? Might have to think about that some more. Needs a bit of polish.