The hardness of an emulsion does not only depend on the emulsion, but also on storage time and on processing:
The longer the storage, the harder the emulsion.
The higher the processing temperature, the softer the emulsion becomes.
So if you process at 25 deg. centigrade, most materials will benefit with hardening. If you process at 20 deg. probably no mayor commercial product needs hardening. The duration of the process also has some influence, so a long Lith session might soften an emulsion.
You can determine if an emulsion is hardened sufficiently easily: if after drying the emulsion feels sticky, it is soft. So process your materials as usual and test afterwards, you can always harden afterwards without problems.
Foma papers are sometimes not hardened particularly well, so after a long Lith session, some hardening might help.