There is no rule against a Life Cleric using Necromancy spells
If there were any such restriction, it would be specified in the Life Cleric subclass description.
Some of the spells Life Clerics gain as part of their Domain are themselves Necromancy spells
It might seem counterintuitive depending on how you interpret these spells, but spells like Raise Dead or Revivify (after Errata) come from the Necromancy school of magic. This in spite of the fact that their sole purpose is to bring a dead character back to life—and not to "undeath" like a zombie, but full proper life. By the laws of the universe, as written in the 5th edition Player's Handbook, bringing a dead soul back to life is considered a kind of Necromancy magic (or Transmutation, if you're a Druid casting Reincarnation to bring someone back to life).
All Life Clerics, once they reach the appropriate levels, gain these two spells (among other spells) as spells they always have prepared. If Life Clerics had a restriction against casting Necromancy spells, then it would be nonsensical that this domain would provide these spells to them for free.