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We analyse neutral and charged matter distributions in second order Lovelock gravity, also known as Einstein–Gauss–Bonnet gravity, in arbitrary dimensions for a static, spherically symmetric spacetime. We first transform the charged condition of pressure isotropy, an Abel differential equation of the second kind, into canonical form. We then determine a systematic approach to integrate the condition of pressure isotropy by showing that the canonical form is a Chini differential equation. The Chini invariant, which allows the master differential equation to be separable, is identified. This enables us to find three new general solutions, in implicit form, to the condition of pressure isotropy. We also show that previously obtained exact specific solutions arise as special cases in our general class of models. The Chini invariant does not arise in general relativity; it is a distinguishing feature of Einstein–Gauss–Bonnet gravity. [ABSTRACT FROM AUTHOR]