Lobotomizer cannot get rid of the status where it can be reborn. It can, however, lobotomize the active skill away so it can't use it.
Now, to clear things up on its ability as such. Suppose that when it is summoned, you activate the ability and play a Plate Armor on it (for whatever reason), and it becomes a 3|4. The opponent plays a lightning bolt, killing it. It revives as a 4|2, because that is +1|+1 to its normal stats. Now, you use the ability again, and the opponent kills it once more. It becomes a 5|3. It does not add +1|+1 to the stats just before death, because its health can be reduced at any time. It adds +1|+1 to its original stats, and then stacks. Almost like hidden counters, ticking away at the exact power of this creature.
Maybe +2|+2 works, but remember that its growth relies on its own death effects. Since it already has synergy with
![Death :death](https://elementscommunity.org/forum/Smileys/solosmileys/../../../images/Misc/death18x18.png)
, this strengthens the bond.