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Muon spin relaxation shows spontaneous magnetism in the superconducting state of LaNiGa2. Symmetry analyses imply nonunitary triplet pairing with line nodes and predict a sub-dominant magnetisation consistent with SQUID measurements. In contrast, there is evidence from penetration depth and specific heat for two-gap, nodeless superconductivity. It was proposed to reconcile this by assuming equal-spin inter-orbital pairing. Here we show within a mean-field framework, that this gives rise to a nodeless, two-gap spectrum. We probe the state's stability in the presence of finite inter-orbital energy splitting and derive an analytical expression for the resulting spontaneous magnetisation. Furthermore, we present a detailed calculation combining a realistic first-principles band structure with a pheonmenological pairing interaction. We find that equal-spin pairing between certain Nickel d-orbitals can describe the specific heat quantitatively. We predict the two-gap structure in differential tunnelling conductance and the size of the spontaneous magnetic moment.