I am a director of a Limited company (SPV) which owns an investment property on a Limited Company Buy to Let. I am one of four directors, other directors are parents and sibling. I don't own a residential property.
Am I eligible for a Lifetime ISA?
Most probably you can. As you don't own the SPV outright you probably can.
If you owned a company or had a trust that owned residential property that you are (or were) able to live in, you're also not considered a first-time buyer.