I'm not the most aggressive connector, but 4 hours in ORD seems like way more than enough time (way too much imo).... I see the responses above where there are some concerns but personally I would do it even with anything more than a two hour connection... but of course YMMV.
Also, if you are connecting UA to LH won't they interline the bags? If so, then geez, I would be down to less than 2 hours.
And, if your incoming is so delayed, then likely the outbound will be delayed also so no biggie.
Let us know, and enjoy the LH F!