Yes, the second words are in partitive, though they are also in plural whereas the first ones are singular.
I believe this is consonant gradation, yes. :D
The ending of the words differs depending on the word: singular - sing. part - plural - pl. part:
lammas - lammasta - lampaat - lampaita (a sheep)
kynnys - kynnystä - kynnykset - kynnyksiä (threshold/doorstep)
sairas - sairasta - sairaat - sairaita (sick [adj.])
allas - allasta - altaat - altaita (pool
so it's not a uniform rule but many plural partitives do indeed end in -ksia/-ksiä. Some examples of these are laukaus, lumous, auraus, rakkaus, naulaus and kyljys.