Can a lost public key be regenerated from the private key?
Yes for standard ECC and RSA. The private key contains (or deterministically derives) everything needed to recompute the public key. The reverse is designed to be infeasible.
Elliptic curves (ECDSA / Ed25519 / …)
Public key = private_scalar × generator_point. If you still hold the private scalar (and know the curve), regenerate the public point anytime.
RSA
The private key structure includes the primes (or CRT coefficients) from which the public modulus and exponent are known or reconstructed. Public key alone never yields the private primes.
What you cannot do
From a public key or address alone, you cannot recover the private key (that is the hardness assumption). If both are lost and you have no seed/backup, the keypair is gone — like the Ring cast into the fire.