Based upon my experience the following is an appropriate statement and solution for this problem; but, anyone viewing this post should feel free to add any comments or concerns regarding the appropriateness of the information and procedure given.
Generally, eyebolt lifting capacity is based upon the tensile strength of the bolt at the bolt top end thread inside minimum diameter, which not effected by bolt thread length engagement, with the assumption that a standard size and class nut specified for the eye bolt has sufficient thread length engagement will be used with the bolt.
As a result, your first step should be to determine the height of a standard M12x1.75 threaded nut. Once you have this data you will know the required bolt thread engagement length in a material of equivalent strength to that of the lifting eye bolt. (I appologize for the bold text but this is a critical element in determing your minimum required tapped thread engagement length)
Your next step is to determine how the strength of your tapped hole material compares to the strength of the lifting eye material. The required minimum thread engagement to achieve the full lifting rating with the eye bolt in your threaded hole is based upon the inverse ratio of your material's strength to the fasteners' material. i.e Lmin hole = Lmin Nut X Bolt material strength / Threaded material strength.
I hope this helps, but if you have any questions or concerns please post them.