I have rebuild several engines in Germany, mostly german cars like BMW, Audi, Mercedes.
I would say the LS or LQ are very good to rebuild, because the where made for eternity, if you compare with modern shit.
All parts are available, the block is a rock, the enginge is from a tecnical view very simple, so it is absolutely a good idea to rebuild.
But as struateng and b-train correctly correctly noted, it depends on the circumstances.
What condition is the engine in, what was broken, what can you do yourself?
Do you have someone on hand who you trust will overhaul the engine well and economically?
Personally, I would remove my engine myself, disassemble it, inspect it and then see what I need.
Of course, I would have things like refinishing the cylinders done if necessary, but I can do the rest myself and could build my engine into a practical new machine with relatively manageable money.
But it takes a little experience, tools and workspace and then you have to decide for yourself, whether you should install a new oil pump, or the old one is still good. You have to make sure that all the work steps such as measuring crankshaft bearings, assembling with the correct torques, preparing the sealing surfaces and so on are carried out properly.
One mistake at such a rebuild will wreck possibly everthing.
And what the previous speakers said is also correct. It's probably best if you have the money to buy a reconditioned engine and have it installed. Then you have peace of mind and guarantee.
If the engine is in good condition and you have someone who can do it, that's also a good option.
If you don't have much budget, it might be better to get one from the junkyard and install it, but in any case it makes sense to see if the old engine needs to be replaced at all, or whether there is another problem.
So please give us more details...