All depends on the design of the lithium battery and its chemistry. and sure it has way higher discharge rate than lead, for the amp hour rating of the battery, but not for the price. I can get a 35 amp hour battery to discharge 300 amps no problem. sealed agm deep cycle too. and that is only 135 bucks. A lithium iron phosphate 100 amp hour battery can discharge 100 amps usually (some more some less, depends on design, which means individual discharge rate of the cells). And that battery would cost 899 bucks+, usually 1200 bucks. No comparison.
Kodiak can be used for house loads. check it out. and its a lithium ion. panasonic cells I believe.
and yeah of course, you would never ever mix the batteries!! One would charge way to fast after first large discharge taken over by the lithium because of low resistance. But if you have a battery charger separating the lead acid, its totally fine. Really depends. Its totally possible to use both and still isolate them. Takes a bit of work. Unless you use the kodiak. It kicks butt. Hook lead acids straight to it. has its own charging and discharging circuit for the lead acid maintenance. its cool!