I have been told that you can go online with Lufthansa and book a "shadow ticket" which makes a reservation for travel without payment and that you can renew this "shadow ticket" every 24 hours. Has anyone heard of this or know who I could contact at Lufthansa to get this information? Customer service had no idea.
I never heard the term "shadow ticket", but some countries require a return (or onward) flight ticket as proof you are willing to leave the country within the allowed stay duration. Right after you entered the country you can cancel the return flight and get the refund.
I have not heard of this (and I doubt Lufthansa would allow perpetually hold tickets for you at no cost).
What you can do - at Lufthansa and many other airlines - is to make a "price reservation". This "saves" the ticket price for you, and you have the option to buy it at a later date (at today's price) or not.
These options are valid for a limited time (48 hours for Lufthansa) and usually come with a small fee. For example: Lufthansa's reservation is free if you decide to buy the ticket, but if forfeit the option there is a 30 EUR "handling fee".
You can make a new reservation after your option expires, but only for the new, current price - not the original one from your first reservation.
As mentioned above, some airlines may also offer free cancellations during a limited time window - but you should check the terms and conditions beforehand.
A travel agent may or may not be able to hold a ticket for a limited time; but probably not for long.
On some airlines you can buy fully refundable tickets, but those are usually very expensive compared discounted fares. The same goes for "full flexible" tickets that can't be refunded but where you can change the travel date at will.
Still, it's sometimes possible to get good deals with those...