Can Lithium battery act as car battery

Can the above jumpstart battery be used in the car ie replace the car's Lactic acid battery?

Is there any better batteries for car than the current conventional lactic acid batteries?
Reason I ask is when such huge lactic batteries fail, I'll need to call an SoS to come to
my rescue to replace or recharge my car's batteries.  If it's a simple battery like the one
shown in eBay above, I can replace it myself.

Suppose my car's lactic battery really break down (due to leaving the lights on when engine
is switched off), can this eBay jumpstart battery really recover/revive back the car's lactic
battery or allow the car to run some distance (say 20km?)
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Q1: Unknown as the design is not fully shown. That's because the acid batteries needs to be charged, and they can do it on the same leads. In this case, it's a Lithium battery, where you DO NOT KNOW what happens if the car starts charging it back through those leads (12V). My guess is, it's a one way electronic design (that's why there's a special button for the car jumpstart), and it won't charge through the same jumpstart cables.
In that case, it cannot be used to replace it.

Q2: The current car battery is usually still user removable (probably max 5 screws or bolts).

Q3: You are confused here I guess. A car battery doesn't allow a car to run some distance, it's always the engine doing that (unless you have a Hybrid or PHEV). Recovery (or just recharging) is also not the function of this battery, it's again, the engine. You unplug this battery after the engine is running. You recharge your car batteries by driving a great distance.  The matter if you can or can't run that 20 km you mentioned, is depending on how trustworthy your engine is, and how much fuel you still have.
Your car has a LEAD acid battery, not a lactic acid battery.

Your car has an alternator and rectifier that generate electricity and charge the battery when the engine is running.

You need the battery to get the engine running in the first place.  The battery turns an electric starter motor, and provides electricity to the spark plugs to start the engine.  In the old days, you would crank the engine by hand, and a magneto would provide the electricity for the spark.

Q1.  As Kimputer says, you can use this as a replacement for your car battery because the charging circuits are different.

Q2.  You can trickle charge the battery on your own (old laptop power supplies are really good for this).  This could
        take several hours.  
        You can use jumper cables to start your car from another car.  

Q3.  If your only problem is a bad battery, you should be able to run 20 km or more once you have started.  
        A bad alternator, a bad rectifier, or a bad alternator belt can also cause problems that look like a bad battery.

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Note that the rating is 38000 mAh or 38 Ah.  The charging is speced at 12V/1A.  
So it would take at least 38 hrs to fully charge this unit.
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The Tesla uses lithium ion batteries. But of course that isn't a "normal" car and you won't be able to use such batteries in a normal car.
"Q1:Can the above jumpstart battery be used in the car ie replace the car's Lactic acid battery?"


The other suggestions  for Q2 & Q3 are correct
I drive a Volt and it has both a lithium ion battery pack (called the high voltage battery) and a lead-acid, normal car battery.  Why does it have that, you might ask?  It runs the accessories.  It is charged via a plug-in while the high voltage battery is being charged.  It is designed to put out 12 volts, while the high voltage battery puts out way more (I'm not sure how much).  Lithium ion batteries don't charge the same way, so the charging system in your car is not likely to work with a lithium ion battery anyway, at least without some significant alterations.
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