It's a lot easier these days researching the available Irish RC records. There's a lot online:-

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search.ancestry.co.uk/search/db.aspx?dbid=61039

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search.findmypast.co.uk/search-world-Records/ireland-roman-catholic-parish-baptisms

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churchrecords.irishgenealogy.ie/churchrecords/

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registers.nli.ie/

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The last site has a useful map format so you can see when available baptism registers begin. Presumably where the Lyncheys came from the registers begin after they left Ireland.