Our initial approach will be to just replace the t-LMF in LH20t by an n-LMF while keeping the other aspects of the functional unchanged. This should enable us to see the effect of the LMF in a particularly direct way. The n-LMF will be trained against atomization energies and reaction barriers. The second improvement we will report here is to replace the B95c DC part of LH20t (see below) by a more flexible B97c-type 50 power series expansion. The reason is that we found the B95c 51 parameterization of the recent LH24x functional (based on an x-LMF) to differ substantially from that of LH20t, and this mattered for the performance, in particular in the context of nonco-valent interactions (NCIs) in the interplay with dispersion corrections. Combining the new n-LMF for the NDC term with the more flexible optimized B97c-style DC contribution results in the LH24n functional that will be a central result of this work and provides substantial enhancements over LH20t for GMTKN55 performance, without needing a CF! It should be noted that the data used for optimization and training cover neither the core nor the asymptotic regions of a molecule. We should therefore expect no improvements in properties depending on these regions, and at this point we will focus entirely on typical chemical energy differences. Moreover, we have so far not used strong-correlation data in the parameterization, and we do not yet consider RSLH forms.