Scott - I have discovered that keeping them connected like that ALL THE TIME - actually can damage the lead acid one.
@patrol21 One issue I discovered early on - when I was making my own LiFePO4 batteries - is that Lithium's will try to maintain VOLTAGE as they discharge at the expense of AMPS. Lead ACID will tend to maintain AMPS at the EXPENSE of VOLTAGE. On old vehicles this was not an issue - but ECU's are fussy about Voltage. If it drops below 9V whilst cranking it does not matter haw many amps you have. I made an 1120CCA Lithium to prove the point.
I have experimented at having 2 batteries (one to feed the starter and another to feed the rest) - This works very very well indeed.
BUT I had problems keeping them charged correctly. I used a split charging box but somewhere in my logic I was creating a huge surge and kept blowing fuses.
Split charge systems need both batteries to be the same type for a start.
MY ADVICE STANDS. Have a good Lead Acid in. Add a Q/D cable connector and keep a small lithium booster in your jacket (keep it warm). Plug it in to start . Disconnect once started. Recharge teh booster once you stop to keep it 100%.