Looks like you're on 30s, so you've got a basic lift, nothing crazy, but you ARE likely in original axles and hubs. You want a daily driver capable of basic off road use, and we're not talking insane horsepower, we're talking drivability and comfort.

1. Reference motor condition, has this motor EVER been rebuilt, overhauled or ANYTHING since it was put in the truck? If not consider a basic rebuild first and foremost to refresh the motor, hone the block, piston rings, new seals and call it good, don't go insane.
2. Look at your costs, for me I can tell you I can find 350s easier and CHEAPER than I can find LS motors. Remember you're also paying to convert the truck, not just buying the motor.
3. Consider your mechanical experience, I'd not recommend diving into a full motor and possibly Trans swap as a novice mechanic with no help, but a more experienced mechanic this could be a weekend project.
4. What do you prefer? While LS swaps are popular they aren't the best option. 350s are still very common, parts are plentiful, lots of horsepower and torque making options exist for them, they've been converted for EVERYTHING you can think of and can be fixed basically with bailing wire and bubblegum. An LS does also have its place as they're in lots of junkyards so you can sometimes get them cheap and they are a more modern engine, but they come with their own headaches in the shape of computers, wiring harnesses and sensors you may not want to fight with long term.

Personally I say keep the 350, fuel inject it and later on maybe build a stroker motor out of it if you want horsepower. But the decision IS yours