What I know is Bitcoin inflation is already known, it is a decreasing function going to zero in 120 years.
In less than a year it will be less than 5% per year...
You are making a number of assumptions with that.
The first assumption is that the miners and developers will be fine with a system that does not generate the number of additional bitcoins that are generated today to pay miners. Do you think miners will be fine only generating money from transaction fees? And if so, do you feel they will accept a low transaction fee? If not and the transaction fee goes high, how do you feel that will affect desire and need for bitcoins?
The miners are apparently in control of the bitcoin protocol as shown with the current BIP situation. The small handful of miners who constitute over 50% of the network have decided on which modifications to make to bitcoin as far as the blocksize goes and are running with it.
How many bitcoins there will be in the future is really up to them. They have shown that they control the network. The developers are a distant second to them. However both have more control than the bitcoin userbase based has.
Secondly, you are not assuming any lending. All major currencies used in the world today have a fractional reserve system. There is no way to prevent a money multiplier or fractional reserve system arising when it comes to any asset or currency.
You can take someone's bitcoin on deposit, lend it out to someone else, they can buy something from yet another person and if you can get that person to deposit their bitcoin with you, you can lend it out to someone else. Re-lending the same coins increases the money supply.
If bitcoin did become popular, you would have bitcoin lending. And all currencies in the past (tally sticks, gold, etc. tally sticks were mostly a system of credit in any case) and current currencies have/had borrowing and a money multiplier. It has not happened with bitcoin (except in a tiny part) because people are afraid to lend. Due to the pseudo-anonymous nature of transactions, people don't trust to lend their bitcoins out. If bitcoin really became popular, you would have lending and bitcoin would be affected by the same inflation rates caused by ease of lending that other currencies have.
It is not the quantity of dollars in the world that causes inflation. It is the ease to which people can get dollars.
Simple example: If anyone can go to a bank and borrow as much as they want to buy a house, what happens to the price of houses?