How are you supposed to lane as a melee?

How are you supposed to lane versus cancer like {{champion:51}} {{champion:236}} as a melee champion? Using those two on top/mid became popular, but it's nearly impossible to lane vs them as a melee champion. I just played against a {{champion:51}} {{summoner:4}} {{summoner:14}} as a {{champion:92}} and I was just forced to sit quite a few units behind my entire minion wave or I'd get auto attacked. When I was pushed to tower I found myself in sea of traps. When I went all in on her, she either flashed or E'ed away and I got headshot or she would place a trap UNDER me and I'd get snared by it almost immediately - another headshot and CC.
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