As far as i know, li-ion batteries are not more safer than lead-acid...not more shock-proof either(unless you're comparing to those old-style liquid type, they are not even really shake-proof)...
Anyway, lipo pack is actually pretty safe when mounted appropriately, given enough "padding" while keeping them in a good venting environment(if high temperature is expected).. They are massively being used in the RC field(remote control cars/airplane models)..you know lipo pack is safe enough as you know how that kind of environment is
PS: actually, the working voltage of LiPo is 3.7~4.2v, LiFe is 3.3~3.6v, LiLo is 3.6~4.1v..
If li-ion is preferred, than I'd go for some >15A discharge lipo pack.. with 3 in series you get a perfect 11.1~12.6v working voltage
There are many pre-packed lipo packs that come with balance port soldered already, so making the maintenance much easier
added:
Protection circuit is a Must-have for li-ion batteries......unless doing so intentionally for a specific purpose(like what Dave have done to those poor multimeters
)..
For using in in a bike, at least you'd need over-discharge, short-circuit, and over-heat protection/indicator. There are many cheap little voltage indicators(light the LEDs according to the the input voltage) at ebay, just get one and hand solder it to the main output(run an extended wire to put the display on the front so you can watch the remaining capacity on the run)..it would be a nice add-in feature