lower bound of block size towards increased speed of propagation As far as I know there is an upper bound of a block, which is one megabyte, is there a lower bound? 

It was in terms of a race condition that I was considering this. 

Imagine you make a double spend and then you try to propagate a block that contains only your second transaction. If so it would be much smaller, ipso facto easier to propagate around the network and get validated by nodes, isn't that right? 

Maybe someone in the mean time would find a valid block for one containing many transactions, in which case it would be longer than yours, and maybe other miners would extend that- but maybe not. 

Does anyone want to try this out on the testnet with me?
There is a lower bound: Blocks must include at least one transaction, the Coinbase. ;)

The advantage of a smaller block has been somewhat overstated in the past, as it usually doesn't matter much, especially since the relay network got improved with Compact Blocks, a compressed block format that significantly reduces the peak bandwidth required to propagate blocks.

Basically, for a smaller block to have a relay advantage over a larger block the two blocks would have to be found within less than 5 seconds of each other. This only occurs once every two to three days and thus is hardly a significant quantity to optimize for in comparison to the chance of even finding a block to double spend with in the first place.