Happy to have been of help. Let's take a look at your new round of questions:
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>How does one find out if there are lamassu/šēdu in the area and contact/build a relationship with them?
Technically, anywhere that there is sacred land, with a threshold, there will be lamassu and šēdu.
Rather than trying to find out if there are any nearby, what you should probably do is acquire a figurine of one (they're expensive, but can be bought on Amazon, or Etsy) and set it up near a threshold that you'd like one to guard. After you've done that, then you should leave an offering at the figurine and invite a lamassu or šēdu to act as a sentry for that room, house, or building.
Once you've done this, it will just be a matter of leaving additional offerings as necessary and ensuring that you show proper respect to the creature whose help you've enlisted.
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>When does a person get their ilū rēši? Is at birth or later?
This is a bit of a tricky topic.
We don't know for sure if the people of Mesopotamia understood the difference between conception and birth. What we do have, are cryptic references in myths to "nine days" passing during fertility and birthing, which might suggest that they were aware of the nine month gestation process.
If they were aware of conception, and not just birth, then it seems likely that the ilū rēši would have been assigned at conception, accounting for the unfortunate fates of stillbirth and abortion. Otherwise, the moment of birth would have created the supernatural bond between an infant and his or her ilū rēši.
Personally, I operate under the premise that one's ilū rēši are assigned at conception, and that they begin fulfilling their duties at birth. This gives your personal God and personal Goddess a nine month head start, if you will, to familiarize themselves with the trajectory of your life and make decisions on which events outlined in your šīmtu—personal fate—they want to focus on first.
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>What happens to a person’s ilū rēši when they die?
As far as I'm aware, there is no surviving literature about this subject matter.
From what we do know about personal deities, some of them are members of the major pantheon—like Adad, Ištar, and Šamaš—so it seems reasonable that we are not the sole charge of each deity, and on the event of our passing they continue to work with their other charges.
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>Do they accompany them to the afterlife or do they get assigned to a new person?
In Mesopotamian theology our deaths are a transitional period, during which we leave behind the Land of the Living and enter into the Land of No Return. Once there, the Scribe of the Netherworld, Bēlit-ṣēri, checks that we are, in fact, supposed to be there, and then grants us citizenship in the Great City, within which all of us—regardless of our earthly standing—become wards of the goddess Ereškigala: the Queen of the Netherworld.
So, it seems unlikely that our personal deities accompany us into the afterlife. Instead, we acquire a new set of deities in the form of Ereškigala and her court.
As I mentioned above, it seems likely that our personal deities continue to accept new charges after the event of our deaths, forever watching over a cross-section of humanity, of which we were only a small portion.
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>What if a person has to move house after having buried a statuette? Should they dig it up and rebury it at their new home or leave it behind?
If you have become personally attached to the lamassu or šēdu then I think inviting it to move to your new home, and burying it a second time, is perfectly acceptable. If, for whatever reason, you want to bequeath its services to the new owner, then you should leave it buried and teach them the ritual you perform and tell them about the offerings that you provide for it.