data.table: anonymous function in j

You don't need an anonymous functions - you can have whatever expression you want wrapped in { } (anonymous body) in j.

tmpdt[, {
          model <- lm(c ~ d, .SD)
          tmpresid <- residuals(model)
          tmpvalue <- b[as.numeric(names(tmpresid))]
          list(tmpvalue, tmpresid) # every element of the list becomes a column in result
        }
      , by = a]

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Some documentation on the use of anonymous body { } in j:

1. Comment in Examples in ?data.table:

anonymous lambda in j: j accepts any valid expression. TO REMEMBER: every element of the list becomes a column in result.

2. data.table FAQ 2.8 What are the scoping rules for j expressions?

No anonymous function is passed to j. Instead, an anonymous body [{ }] is passed to j [...] Some programming languages call this a lambda.

3. Blog post by Andrew Brooks on the use of { } in j: Suppressing intermediate output with {}