Leighton-Micali Hash-Based Signature key sizes
Yes, each LMS parameter sets can be used with any OTS parameter set.
In the final NIST Recommendation for Stateful Hash-Based Signature Schemes there are even more parameters defined.



Those calculations are correct but we do not need to store the entire LMS tree in memory. The solution is to store the seed for the RNG in the private key and calculate the tree on demand. Requires more work but requires much less memory.


Calculations
LMOTS private key:
Size = 4 byte LMOTS typecode + 16 byte identifier + 4 byte q + n byte seed
Example: LMOTS_SHA256_N32_W8 = 4 + 16 + 4 + 32 = 56 byte

LMS private key:
Size = 4 byte LMOTS typecode + 4 byte LMS typecode + 4 byte q + 16 byte identifier + 2^h LMOTS private key size
Examples:
LMS_SHA256_M32_H5 &amp; LMOTS_SHA256_N32_W8: 4 + 4 + 4 + 16 + 2^5 * 56 = 1 820 byte
LMS_SHA256_M32_H25 &amp; LMOTS_SHA256_N32_W1: 4 + 4 + 4 + 16 + 2^25 * 56 = 1 879 048 220 byte ~ 1.9 GB