From a security perspective, I don't think whether you're on one ticket or two matters
in this situation. You don't need to (re) check luggage, and the security folks just need
to see a valid boarding pass and ID.
Where 1 vs 2 tickets matters is if you are delayed on your first flight and miss the second
one. Then, you're not protected and are at the mercy of LH for how they can get you to
FRA.
There are nuances; what is the ticketing airline for each flight? If they are the same, you
may be able to get a (well-trained) agent to combine them under the same record locator.
If you, for example, booked with $ on AC and miles on UA for the LH flight, no dice, I don't
think. You would be derisking things if you can get your flights on the same record locator.
Your comments about paying for one ticket in cash and the other with miles doesn't make a
lot of sense, though. If you have enough miles to book YVR-FRA, you probably have enough
miles to book SEA-YVR-FRA all with miles, or, as joe32F notes, the direct SEA-FRA flight. Or
some other connection on Star Alliance, such as SEA-ORD-FRA. If you are low on miles and
need to pay cash for the YVR-FRA flight, you might be throwing away miles for nothing,
as I would guess the SEA flight doesn't add much on. But you haven't mentioned dates, so
I am just speculating.