I have only a little knowledge about these scaling solutions so I want to ask if it's possible to somewhat combine these two solutions. Like, change the transaction protocol according to SegWit to allow off-chain solutions (Lighting Network) while letting the miners choose a size of the block. Is this possible?
It's technically possible, as already pointed out by others. But many of the community, including me, consider the Bitcoin Unlimited mechanism to be potentially dangerous as it maybe could lead to network splits and gives the mining pools too much power what could lead to centralization.
"Softer" flexible blockchain proposals are BIP 100 and 106. In
this thread some of us are discussing a possibility to restrict miners' power in BIP 100 even further by imposing a hard-coded upper blocksize limit that only moves in slow steps, in addition to Segwit.