Alan, you've got two different issues going on in this thread.
In the first you are mixing diatheseis (voices). The subject functions differently in 'I have untied something' and 'I am untied'.
On 'breaking down' a verb you're looking right through the language and maybe trying to reconstruct history of the language.
The forms in question are λαβεῖν λαμβάνειν and εἰληφέναι. It is immediately apparent that the word has a λ, a non-high, non-back vowel (α, η), and a consonant formed at the lips (β,φ).
Beyond that the two 'funky' items are the relationships between the different forms. The aorist stem has a couple of nasal sounds added in order to make the continuative. The perfect stem uses a vowel reduplication 'ει'. Someone learning Greek as a language to use does not need to know when and what processes caused the resulting forms. Instead they simply use the forms at hand. This particular word λαβεῖν needs the three infinitives listed above in order to know how to use it. In addition the future λή(μ)ψομαι λή(μ)ψεσθαι is necessary. Yes, the diathesis changes.
At a later stage a student can work with the passive system of this verb. λαμβάνεσθαι, εἰλημμένος εἰλῆφθαι, λη(μ)φθείς λη(μ)φθῆναι.
I recommend that a student/teacher/classroom only work on one piece at a time. The students don't even need to know what lurks in the future while they are working with λαβεῖν and λαμβάνειν. And in any case, a teacher/student certainly wants to learn each of these forms as they are and to work with them, long before any attempt is given to tracing the historical development of the forms and any "partial rules" that halfway account for the forms.
PS: for typing Greek you need to activate the Greek Polytonic keyboard (windows) and (Mac). Then learn to type with those key positions. Stay away from any and every proprietary keyboard system as you will end up frustrated down the road, as you've just encountered. Using the Greek national keyboard will allow you to type Greek on any computer anywhere in the world (assuming that they are using 21st century operating systems). (PPS: in Greece you may need to activate the POLYTONIC keyboard, since most computers there default to the monotonic (single acute accent) keyboard. Of course, you can type comprehensibly with the monotonic keyboard, it will just be leaving off the breathing marks, circumflex and grave options in writing. Everything else is the same.)