You need to restart the process of acquiring ritual spells via this mechanic.
The process of copying the spell into your ritual book takes 2 hours
per level of the spell, and costs 50 gp per level.
The feat mentions this.
When you choose this feat, you acquire a ritual book holding two
1st-level spells of your choice
This occurs only when you choose the feat.
Afterwards the content of the book, a physical object, is governed by the process described above. So if you lose it, your only recourse is to find more spells and use the rule above to scribe rituals into a new book.
As a general comment, the gist of the game is for the referee to present a setting for the player to experience as their character. In this sense it is a pen & paper virtual reality. This relates to your question in that given the lack of specific rules, you should consider the issue as if you were really there. The Warlock getting his Book of Shadows (PHB 108) is an example of a specific exception to the assumption of a pen & paper virtual reality. In this case the character has a physical book filled with ritual spells. Lose the book and you lose the spells and have to spend time and money to make a new one.
Note that there appears to be no initial cost assigned to making a new ritual book. However, in the equipment list a spellbooks cost 50 gp, and a blank book 25 gp. Personally, I would charge a PC the spellbook cost for a new ritual book. However, if you are not comfortable with that then charge the player the cost of a book. Other than that, there is nothing to prohibit characters from spending additional time and money to make a backup book.
Also, this is consistent with how the Wizard spell book works on page 114, which is the closet relevant mechanic.
Of interest is that the ritual feat is the only way for a sorcerer to cast ritual spells, as he doesn't possess a ritual casting feature as a function of class as far as I can tell.
No.
On your adventures, you can add other ritual spells to your Book of Shadows. When you find such a spell, you can add it to the book if the spell’s level is equal to or less than half your warlock level (rounded up) and if you can spare the time to transcribe the spell.
You can inscribe spells that you find. Which implies they must be written down. As a warlock spells you know, you gain magically through your pact to your patron. Those you don't understand in a way that can be expressed in text.
This is also been answered by Jeremy Crawford here: http://www.sageadvice.eu/2016/04/26/book-of-shadows/
Work Around
If your DM allows scroll scribing/magic item crafting, you could create a scroll and then copy it into you Book of Secrets. This could be very expensive as Common items (Cantrips and level 1 spells) require 100gp, and minimum level of 3, all the way up to Legendary items (9th level spells) requiring 500,000gp and a minimum level of 17. 5th level spells (the max for a warlocks spell slots) are rare, require the character to be level 6 and spend 5,000gp.
Best Answer
RAW is unclear
Pact of the Tome reads:
And book of Ancient secrets reads:
The rules for replacing your Book of Shadows are vague and by my reading of the RAW there are four possibilities. (Tweets by D&D designers confirm the first is correct).
Your replacement is just like your old book
This is I would argue both a valid reading of the RAW and probably the RAI. The rules neither say the new book is empty nor do they say it is full but they do say it is replaced and the best replacement would be an identical book. I would argue that a blank book could not be considered a replacement for a full one (I would certainly be pissed if someone gave me back a blank book when I lent them "Name of the Wind").
Mike Mearls asserts that this answer is correct, and Crawford confirms it.
Your book comes back with no rituals
Probably the strictest RAW interpretation is that you get a blank book back but still have access to the same three cantrips. The pact does not explicitly state that the cantrips are recorded in the book only that having your Book of Shadows on your person allows you to cast them at will. Therefore they will neither change nor go away when you get a replacement. Nothing in the description of the replacement says you get to keep your rituals though.
Your book comes back completely blank
This is both the harshest and I think the least likely correct interpretation of the rules but for the sake of completeness I'll include it. The biggest strike against this reading is that you would lose the cantrips.
Your book comes back and you get new cantrips and rituals
You could argue that because you get a new Book of Shadow you have a new instance of the ability and gain new cantrips and the two free rituals. Again I don't think this is correct but it's not an unreasonable reading of the rules. The primary breaking point of this reading is that you could cycle through all the rituals and cantrips while having your wizard copy them down or just summon a new tome when you find yourself in need of a ritual you don't already have (it would functionally just take 1 hour and 10 minutes to cast instead of the 10 minutes).
Protecting your spells
If you are using the first interpretation (which we do at my table) there is no need to protect your spell as you will get them all back with your new book, otherwise there are a few ways to protect your spells, most are just ways to get copies of the spells in your book. Most require the help (paid for or otherwise) of a non-warlock character.