In at least one version of the Lilliput story, her transformation to mousegirl takes place in the Rescue Rangers universe-- so, naturally, they'd take her in and give the poor naked mouse something to wear! Not necessarily the best fit, given Lilli's figure compared to Gadget's, though...

A fun artwork by the mousdorable Matthew the Mouse, who has my thanks and clearly likes a mouse with some curves. Posted with permission.