In domestic use LiIon (Lithium Ion) batteries are, all things considered, MORE dangerous than "lead acid" batteries, not less dangerous. But both are "reasonably safe" [tm] when used properly.
The advice that you linked to above is actually titled "What precautions are needed when charging a car battery in an apartment?" and that is quite different than charging a car battery at home.
Specifically, a car battery is a one of a range of variants of lead acid batteries and contains liquid acid and while it has plugged vents and fillers it is not "sealed" in any adequate manner. Under certain conditions which are reasonably liable to be encountered in normal charging it may liberate either acid fumes or Hydrogen gas, or both. If it is charged in a car or outside it is unlikely to cause many problems.
Lithium Ion batteries when being charged do not usually liberate hydrogen or release electrolyte. Both are possible, but only if a damaged or incorrect charger is used. In exchange for not doing these things. instead they occasionally catch fire and "explode" - actually not a true explosion.
Each 18650 cell in a typical laptop battery contains the energy of about 12 high energy load '44 magnum' shells or about 24 "standard" .44 Magnum rounds, and that's just the electrical energy. (The energy from combustion can exceed 300 kJ, or over a hundred .44 Magnum rounds!). An entry level netbook has 3 such cells and a top notebook PC may have 9 or even 12 of these. This can be released in about 10 seconds with flame and 'lots of heat'. The standard industry term for this, somewhat tongue in cheek is "Vent with flame". The fact that a standard industry term exists indicates that it's a well known problem. The "melt down" mode can be triggered by charging to too high a voltage, discharging excessively and then charging normally, charging at an excessive current rate, puncturing them, or in selected cases* giving them a slightly harder than usual knock which causes internal parts to short together and - Wow!. (* This is obviously a manufacturing fault but has happened in a number of independent cases due to too tight manufacturing tolerances and substandard assembly).
All that said - given how many there are, LiIon batteries have proved to be very safe considering how many there are and how they are treated. Despite the horror stories I have never seen a real world "vent with flames" event.
Added 7 years on: I've now seen one. An old netbook with a dead LiIon battery pack was left connected to a power supply for several days. One evening it sudeenly burst into magnificent melt-down. Flame, smoke, ... - urgent defenestration of the battery save the netbook - and the couch was "not badly damaged". Had we not been in the room we'd have had a house fire.
Lead acid batteries do not have an equivalent failure mode to "vent with flame"
However, drop a spanner, vacuum cleaner metal suction tube or similar across the terminals of a car battery and you'll get immense energy release. The battery may be damaged by such treatment but usually won't explode. Charge them too fast or too long and Hydrogen gas will be produced and WILL leak out and can form a flammable or explosive mix in confined spaces. Battery acid from other than fully sealed lead acid batteries seems to be special Houdini grade - skilled at escaping in many unexpected instances. If you carry the battery and your arms itch, Wash them NOW. Next time you wash your clothes small holes with brown edges may appear(Ask me how I know). Charge them inside at above gassing point and you may be sorry. I was :-).
BUT Lead acid are also very safe as long as they are used as intended. Charging a wet plate lead acid car battery "inside" at home is not included in "as intended".
Some excellent related links, recommended by Nick Alexeev:
MPower UK - Lithium Battery Failures
SE EE - Why is there so much fear surrounding LiPo batteries? - good question and eleven good to great answers.
Without further details it is difficult to tell.
Anyway, there is a BIG caveat: jump starting a veichle requires very high current spikes, and the cells in the string must be able to withstand it.
If the lead acid batteries you will use are of the starter type (and not of the deep cycle type, as used e.g. in UPSs) they are designed to provide current pulses that are even hundreds times greater than their normal current rating (e.g. a 50A rated battery could provide 1000A pulses for a couple of seconds).
This is a problem with LiIon cells, which usually can't survive such pulses. You might think that putting in series an equally rated 50A LiIon battery would do, but probably that battery could survive just a 200A pulse, and maybe for only a few milliseconds).
Moreover, the internal impedance of the LiIon cells could be greater than that of the Lead Acid battery, so you end up with a pulse of power being dissipated in the LiIon that could raise its temperature above safe limits.
See this comparison table between rechargeable batteries at BatteryUniversity.
TL;DR: you should get the datasheets of both the Lead Acid battery and of the LiIon battery and examine their characteristics. Only then you/we could tell if what you have in mind will be safe to do.
SAFETY WARNING: lead acid batteries are quite rugged and they can withstand even strong overloads for a short time. LiIon CAN'T DO THAT Overloading a LiIon cell could heavily damage it, which in turn could make the battery explode or vent with flames!!! Don't try your experiment without knowing the characteristics of your batteries. You don't merely risk to damage your batteries, you risk your life (especially with big LiIon battery packs)!
What you propose should work technically and is probably not too hard to do "well enough" as long as you are sensible [tm].
As Peter says, mixing battery chemistries can often have bad outcomes, but as long as you do not violate basic requirements this could be reasonably problem free.
It is not obvious why you would use a LiIon second battery - lead acid will better match the cost/capacity and general cycle lifetime for given use.
If your main battery was say about 50 Ah (less than 1 hour at 50 A due to C rating usually being at 10 hour rate or even lower) and you wanted both batteries to work together throughout the LiIon battery would also need to be 50 Ah or more. That's not a small battery and you are going to need a separate specialist charger to charge it - which is OK if you have the equipment already - but otherwise adds expense and complexity. You may be able to obtain 2V indivual LA cells or a 4V battery (they do exist) but again are faced with the charging issues mentioned below.
A LiIon battery MUST have it's low voltage discharge limited to a safe voltage. It MUST be rated to discharge safely and continuously at say 50A.
Max charging current is liable to be 25A or 50A (or other - varies with manufacturer). You COULD safely enough [tm] charge a single LiIon cell by limiting Imax to at or below rated max value and setting maximum charge voltage to say 4V or slightly less. You can then allow it to charge until 4V is reached and can float it at 4V "safely". This charges to noticeably below max capacity and increases cycle life. You MUST NOT charge it all the way to 4.2V and float it there - battery death happens soonish.
Note that LiIon will have 4.2V (if fully charged) to start and 3V or so fully discharged. (Lower possible but unwise if long cell life is wanted).