Lag and peak power are dictated by the size of the wheels AND the housing size.
Common garretts usually come in two sizes, 3 n the reeaaally big variety of turbos. .63 and .82
the thing with ebay turbos is theyre very mismatched wheel and housing wise (there are some good ones however), and they twnd to be of heavy cheap materials, hence the lag.
If you knew the exact details of yiur current one, measuremwnts etc, and where it came from, theres no reason why you couldnt chanhe the housing and reduce the lag. But, if it is an ebay turbo, it might be difficult to sourve a housing for the correct wheel.
Therefore you might be better off sourcing a new one, carefully.
It will be worth taking it off to have a look, it looks accessible.
Just had a thought, with strange housing a/r ratios like that it could be some variety of holset turbo, theyre quoted as cm^2 size, and very innacurately converted to an A/R figure.
Unless you can find out exactly what it is from previous owner, i say take the thing off and inspect it.
Its also worth noting we dont know the general condition of that engine, and there may be another factor affecting spool/boost.