Lie algebra associated to Leibniz algebra

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We know that for any Leibniz algebra $L$ we can associated its Lie algebra denoted by $L_{Lie}$. for example the ideal generated by $\{[x,x] | x\in L\}$ determines the non-Lie character of $L$. Is it possible to find the ideal which is the largest ideal of $L$ determining the non-Lie character of $L$? if so, how can we find that?