If one has the last round key in an SP or Feistel network (the 16th round key in DES for example), would that someone be able to decrypt the rest of the encryption?
It depends on the block cipher in question - specifically its key schedule. Knowing any round key of AES-128 would let you calculate the key, because the schedule is reversible. OTOH, e.g. TEA would retain secrecy of most of the key and might remain secure, because its round keys are small enough parts of the key.
In the case of DES, it is weak enough to be decryptable regardless of any information. However, knowing a round key would make it trivial, since every round key reveals 48/56 key bits, leaving only 8 bits to be brute forced.