Diamond is easier to find if you can find virgin land that nobody has mined yet. Dig down to the bedrock, then go up a few levels (4 or 5) and start mining channels, you'll find more diamond in those strata.
As for losing things to lava, I never go deep mining without two buckets of water, either to pour on lava blocking my progress or pour on myself if I get it really wrong.
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And if needed with two buckets of water you can make an infinite amount of water, which is why I carry two not one.