Can one use a Cryptographic Accumulator to efficiently store Lamport public keys without the need of a Merkle Tree? One of the problems of one-time Lamport signatures is that public keys are disposed after use, so you must generate many keys and store them in a Merkle tree. The root is the "real" public key and each signature is supplied with a Merkle branch from the root public-key to the one-time public key.

I was thinking of using a cryptographic accumulator to store efficiently the one-time public keys. The root public-key would be the the digest of accumulated one-time public-keys. A signature would only include the proof that the one-time public key belongs to the accumulator. This proof may be shorter than a Merkle branch if the number of public keys is over 256, for comparable security thresholds.

The only drawback I see is that known cryptographic accumulators (e.g. Benaloh and M. de Mare) are based on number-theoretic assumptions (such as factoring), and using Lamport signatures one is usually trying to avoid those assumptions, probably to get quantum computing resistant schemes.

Nevertheless, I suspect there are cryptographic accumulators which are quantum computing resistant, so the argument may not be strong enough.

To summarize, may cryptographic accumulators serve as a more efficient method to distribute Lamport public keys ?
Yes, they can be used for that purpose.  The challenge in practice is exactly what you mentioned: if we're willing to trust number-theoretic assumptions, we usually don't need Lamport signatures.  Nonetheless, they can be used in this way.