Since your question doesn't involve any information about a shuttle, I presume you are looking at mounting this permanently in your boat and maybe having the battery under the counsel or something in that form factor. If considering drill batteries to provide power in this situation, something to consider is both accessibility to the batteries and the likelihood of forgetting the batteries at home on the bench on the charger. Whereas if you were to go with a standard lithium battery mounted under the dash, you can leave the charging cable in the boat attached to the battery and plug it into your shore power to charge both that, and your other on-board batteries at the same time. Running a dual drill battery setup, the likelihood of not charging a second battery, or forgetting the batteries at home could potentially increase the number of quarters into the swear jar at the boat landing.
To run the application you are presenting, and presuming not continuous use, here is some information that may be of benefit.
10" Screen and Livescope - 30Ah for 10 hours. 32Ah for 13+ hours. 48AH for 19+ hours.
If you are switching this unit on and off throughout the day, you could likely get away with a 20Ah battery. If you have intentions of leaving it on all day, I wouldn't consider anything less than a 30Ah battery.
Alternatively, if you are running a shuttle setup, most shuttles now days have a space built in to contain the battery, and most shuttles do accommodate up to the 30Ah batteries with ease. This creates less weight and overall bulk as a size factor. Between the mounting of the graph, black box, and battery/cabling, it could potentially lead to some fabrication issues to try to accommodate the drill battery system and you still run the risk of forgetting to charge items or forgetting them behind on the bench. When I ran my 126SV and LV32 setup on a summit fishing shuttle, I ran an amped outdoors 30Ah lithium battery. I added a 2-terminal plug to the battery and hung it out the back of the bag. When I would plug in shore power, I would split off another drop cord to the shuttle and charge my lithium at the same time. I could fish an 8-hour tournament with the pack on all day and still have plenty of battery left to spare.
At the end of the day, it is up to your budget to determine the route you want to go, and no matter the route you take, make sure to put an inline switch in place to shut power off to the black box while it is sitting idle, or it will drain any battery it is hooked up to.
Have fun!