My current understanding is that Atomic swaps will allow exchange between multiple crypto currencies in a trustless way without the need of a third party.
If Lightning network is going to be a requirement to activate it. Does it mean that It's going to be impossible to trade ETH to BTC as ETH has no LN? Atomic swaps have to be developed in each currency in order to be able to use it to exchange?
Indeed. ETH could have it's own type of Atomic Swap mechanism, but it likely wouldn't be compatible with the Lightning implementation. Some coins can already do Atomic Swaps without Lightning. I recall Burst and Qora did it what seems like ages ago now, then Litecoin and Decred did it earlier this year. So there are definitely workarounds that don't involve Lightning, but I get the sense that Lightning's method will be comparatively easier and more convenient.
To confuse matters, apparently there's a distinction to be made between "on-chain atomic swaps" and "off-chain atomic swaps". On-chain atomic swaps have to have the same hash algorithm for both coins. Off-chain atomic swaps won't have that limitation.
There's probably still time for some standardisation to occur, since it's all still very much in its infancy. With the immense network effects that Bitcoin commands, that will probably have the biggest influence on how most coins try to implement it. It's fair to assume most coins would want to be compatible with BTC if they can.