Touchscreen won’t be the battery killer. Bluetooth will drain it though, and will drain the battery on the phone also. Though if you don’t want live tracking and want upload at end of the ride, just turn off Bluetooth on both until you need it.
Make sure backlight is turned off also.
510 will talk to Garmin’s app on a phone, and I find battery can last a good day of riding. 10hrs+ easy. It has a basic touch screen but you can lock it so it’s not going to get messed up while riding, especially if you stick it in a pocket or backpack. Has buttons also, which actually concerned me that they might get knocked as they don’t lock, though they’ve been fine. I’ve heard some newer Garmin’s have the buttons on the sides and some have had problems with bar mounts and knocking the buttons with knees etc.
Biggest problem you’ll have is the shockingly poor pairing ability of a Garmin over Bluetooth. I give up and use a cable on my PC. It’s really not that much hassle. Connect Garmin, drag files to computer, upload to relevant web site. I don’t use Garmin Express software. Messes up things on the computer and also auto updates the Garmin with new firmware which can mess that up big time. Always wait numerous versions after firmware release until you can conclude that it’s stable, and even then it probably isn’t. Garmin do nice hardware but terrible software.
No idea about Lezyne.