Not only LP, but all values in Yu-Gi-Oh are rounded up after being halved while odd.
Unfortunately, official sources verifying this are either nonexistent or are very difficult to find; however, this is something that can easily be verified by halving ATK, LP, etc repeatedly in any officially licensed Yu-Gi-Oh game - such as Duel Links or Legacy of the Duelist.
If I find any direct footage of this occuring, I'll add it to this answer right away.
EDIT: So, I wasn't able to find footage, but I was able to find this:
In the card rulings for Solemn Judgement, under "Previously Official Rulings", we have:
If halving your Life Points results in a fraction, your Life Points are rounded up.
Now, of course, this is a previously official ruling, but unless there is a ruling that directly states to the contrary, this ruling can/should still be considered correct. This also technically is a ruling for Solemn Judgement specifically, but I think in this case it's a safe assumption that the idea is extensible.