I ran a Peterson 3 gallon tank and their breather for my LS7. You can also buy a used dry sump tank from eBay off of the NASCAR parts sellers.
Be advised that the factory LS7 pump has issues with the physical cover that bolts up to the pump deflecting under high pressure and allows oil to squirt/cavitate out. On mine above 5,000rpm it wouldn't increase above 55psi when hot and out on the track beating on it. The fix is a Katech LS9 pump and billet cover they make $$$. It is also advisable to run an Aviad or similar oil pan as the factory LS7 pan has its shortcomings even when running a helper setup like you are describing.
This is the main reason I sold my LS7.... and am doing the Dailey billet system and a new engine build.
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Project: 1969 Chevelle, alum 5.3, GTS76 turbo, Chiseled Perf A/W intercooler, Holley Dominator EFI, Davis TC, JRi coilovers, 14" brakes, T56 Magnum. CTS-V Recaro seats!
Coffey Fabrication Nashville, TN doing the fabwork! 800rwhp+/25mpg+/9's@150mph goal 
https://lateral-g.net/forums/showthread.php4?t=52976
1993 Mazda FD RX-7, built LS7, T56 Magnum, Holley HP, Davis Tech TC, 8.8" 3.73 Cobra IRS diff, DSS axles, Ohlins coilovers, big brakes.
CCW 18x11 front 315/30/18's and 18x12.5 rear on 335/30/18 RA1's, 2850lbs
10.31@137mph 165mph Shift-Sector 1/2 mile speed
441ci AllPro headed motor and 200lb weigh reduction in the works....
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