black valve cover D16A1 from a 88-89 integra is 118 horsepower...
the brown valve covers in the 86-87 had 113
as far as swapping, you could look for a ZC or D16A8, or D16A9, these are euro or JDM motors and will net about 140 horse...
if he wants 150-170 then you;re talking money, BIG MONEY
an LS swap from a 90 integra will net you 140, but you need lots of modification, for more info on ANY b series swap into an 88 integra check hasport.com, they sell the mount kits and have good instructions for the install
cheapest biggest horse = h22 swap approx 2000-2200 for an h22 swap, then mounts, shift linkage to shifter cables, cable to hydro clutch conversion, OBD0 to OBD1 wiring conversion.. etc etc etc
plus axle modification, and i;m not sure if they make a kit for an H series into an 88 teg...
if you are good at fabrication you could make a ton of money setting him up with a custom turbo kit...
you can use the HF manifold with any turbo, junkyard intercooler, etc etc etc, and he should be able to get to the 150-170 range... higher with proper tuning...
or you can look for a set of cams to get him to maybe 130-140 if you open up the intake and get a header for it... a port and polish will also add some horses...
you're talking a lot of money for just about every motor swap except for the ZC or D16A8/9 but these motors are kinda rare and be ware of getting ripped in the ass if you don't know your honda blocks...
you can also take his motor and swap in the internals from the above mention D series motors to get him some more horses
i think the cheapest choice other than the D series would be a B16, nets 160 horse, fairly cheap motor, still need mount kit, can get a B series cable trans... but the B16 has low torque and i think the early integras are a semi heavy chassis... but if he has the money and oyu have the time go for the B16, it will put a smile on his face and get your paid...