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For ethereum mainnet, there is "relay" for sending bundle, e.g., flashbots relay. But is I cannot find such thing for L2 chain such as Base chain.

Is there any relay for Base chain, or relay is not needed for L2 chain?

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There is no MEV on L2s with centralised sequencers.

You can send your transaction directly to the sequencer.

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MEV currently stands for Maximum Extractable Value, and rely on ability that the validator have to reorder the transactions to extract value.

Flashbots have its own archictecture based on researchers, builders and relay to mitigate the negative externalities posed by MEV, this concept is related to the archictecture called Proposer Builder Separation (PBS).

L2 use sequencers that basically receive trransactions and form a queue, usually First In First Out (FIFO), then there is no possibility to reorder transactions, so really no MEV.

An comment from Arbitrum FAQ explaining their sequencing:

Since transactions are processed in the order that the Sequencer receives them, no priority fee is necessary for Arbitrum transactions; if a transaction does include a priority fee, it will be refunded to the transaction's origin address at the end of the execution.

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