Lets look at some micro-cycle times:
120 seconds is the micro-cycle time for your breeder reactor. Then we bring up this cooling reactor, which has a micro-cycle time of 500 seconds even. Pushing that to 125 so it is an even 4 reactors is NOT safe, unfortunately, so you'll need 5 cooling reactors for this setup.
If you double-check the last page of the DDoS reactor thread, you can see a doubled 5 chamber reactor which can handle this in two reactors for an overall savings in materials expended.
It is basic math. Lapis is a finite resource. Eventually, it will run out. You can't NOT run out if it runs long enough. Finite resource expenditure is ALWAYS better than negative resource flow.
Lapis is used in bulk when trying to make MFSU's, which is going to be necessary when dealing with the quantities of power that you start working with when playing with Nuclear. 10+ MFSU's is not an unusual number to set up in serial to be able to avoid choking your EU flow. MFSU's require Lapotron Crystals. LOTS of them. Trust me, if you start actually building the infrastructure you're going to need to support this, you're going to be spending through quite a bit of your lapis.
Tinkers Construct is a stand-alone mod which focuses on more 'low tech' tools. It has a different method of enchantment which consumes copious quantities of resources in order to put enchantments on the tools. However, it doesn't play nice with GregTech, the mod authors got into a pissing match, and installing one pretty much guarantees you won't be able to install the other.