Needed fragments for blue lagoon: 300
Base daily production: 10
F(A)SP-items can't be used for additional collections of blue lagoon fragments
Assuming the strategy to use the blue lagoon + BG is used to speed up the collection of the next blue lagoon. Using the other guaranteed double collection to get double fragments for blue lagoon for the 5 it's usable collections.
Further more assuming ultimate luck with double collection with BG so, every collection with BG to get blue lagoon fragments is doubled and the GbG champion building's production too:
10
base production x4 (BG+blue lagoon double collections) x 5 collections = 200/300
100
are still needed / (10
x2 BG's double collections) = 5 collection cycles w/o blue lagoon
So, in the best case scenario a player would have every 10 collections half of the time the blue lagoon's guaranteed double collection for 1 single building besides speeding up the next blue lagoon.
300 annual collections x2 BG double collections = 600 worth of collections
150 annual collections x2 blue lagoon's doubled collections = 300 extra collection worth
So, in total upmost a player could get worth 900 annual collections from a building of choice.
Current meta
Assuming the player picks a lvl2 GbG champion building:
600 worth collections x 10
/collection = 6.000
/ 500
needed per GbG side building's selection kit = 12 kits or 6 lvl2 buildings at most
Renewable blue lagoon
Assuming the player picks a lvl2 GbG champion building:
900 worth collections x 10
/collection = 9.000
/ 500
needed per GbG side building's selection kit = 18 kits or 9 lvl2 buildings at most
So, in the current meta with ultimate luck with consistent double collections annually 6 lvl2 GbG side buildings are achievable. If blue lagoon can be produced from a 1-time settlement main reward building its increased from 6 to 9. So, just 3 extra buildings on an annual basis. Which isn't terrible much considering power creep. While it does speed up progress of a building of choice.
With the dreaded Neo colossus lvl8 this would mean at best from 1,8 marble selection kits to 2,7 at an annual basis. Basically pretty much 1 fully levelled after 1 entire year at the sacrifice of 1-3 additional GbG side buildings of a lvl2 GbG champion building is present.