Bravo!

Initially I tried to mash up the original lines that followed each of the starting pair, but the best I could do with them was

That there's some corner of the Lord I pray has taken me.

which is (a) twee, (b) doesn't really manage to squeeze in several of the most distinctive parts of either original line, and (c) ends up rhyming ‘me’ with itself which is clearly cheating.

After some thought I decided to head in a different direction completely, so my revised attempt at a second line is:

“Twit.”

That there’s some corner of a foreign field where I'm asleep

(OK, doesn't *quite* rhyme)

If I should die before I wake, think only this of me:
As plurdled gabbleblotchits on a lurgid bee.

It doesn't really make sense, but:

If I should die before I wake, think only this of me:
You shit, Death, stop fucking porlocking me!

Let's find embalming fluid that is safely gluten free.

I am not there; one short sleep past, we wake eternally.

"I warned that bloody Annie that I'd lay me doon and dee"

Abandon hope all ye who enter this forbidden tree.

I wanted to try to mash up the lyrics of Enter Sandman and Disposable Heroes, but couldn't find a good rhyme for "me". I mean, there's "Victim of what said should be" but even if I try for four lines I can't quite get it to work.