However, if Liteserver receives a DMCA email from the United States, they must process it, while other Dutch merchants can ignore DMCA unless they violate their country's laws. Why is this?

Like Jamph said, same with Netherlands too. @LiteServer has explained in their discord that they do not follow US DMCA but NL has their own equivalent DMCA Law that they have to abide by.

LiteServer: NL -> https://liteserver.nl/virtual-dedicated-servers/

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https://liteserver.nl/ (Relay, Exit, Crypto)

Liteserver.nl

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In the past I used also liteservers, alwyzon and others.

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LiteServer @LiteServer

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Liteserver.nl

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sales@liteserver.nl

@NetDynamics24 @LiteServer

sales@liteserver.nl