Hi,
Yes, a TR4 can be lowered pretty easily.
It will handle better if dropped an inch or so. (I'd not lower much more for a street car.) This is larger just a factor of lowering the car's center of gravity.
On the front there are several options. And, there are heavy duty springs available that are 1" shorter than stock, but really don't lower the ride height. Those HD coils can be bought in lengths for use either with or without the stock aluminum spacers.
I don't recommend just leaving out the spacers entirely with either the stock or the uprated front coil springs that are designed to use spacers. This would leave the springs too loose at full extension and they might jump off their perches, and will probably lower the car too much. (1-1/4" spacers removed would drop the car about 2" in the front, I'd estimate.)
One method, at least partially, some folks invert the lower a-arms. It's easily done while the front suspension is disassembled. All that needs to be changed is the stud at the inboard end needs to be moved to the opposite side of its a-arm, then swap around the a-arms to install them "upside" down. Personally I don't like this idea much because it also increases the distance from the bump stop to the bracket on the spring tower. This will allow more wheel travel, so be sure to check wheel and tire clearance up into the wheel well very carefully if you go this route. It will lower the car roughly 3/4".
Another option is to use the shorter alu shims The Roadster Factory sells, in place of the 1-1/4" stock aluminum spacers. They sell them to fine tune ride height on the IRS cars and offer them in several thickness (1", 3/4" an 1/2" if memory serves) as well as in diameters to fit both front and rear of the cars that have coil springs on all four corners. The 3/4" tall front spring spacers will lower a TR4 approx. 3/4", although only 1/2" shorter when compared to the stock spacers. This is because of the gemoetry of the front suspension.
You can also have a machine shop custom trim your existing spacers, to set the ride height more exactly where you want it. Keep in mind that about 5/8" reduction in height of the spacer will equal close to 1" drop in the car's ride height.
You can also have the coil springs shortened. But, keep in mind that doing so will also increase the spring rate and, again due to the gemoetry shorten about 5/8" to drop the car approx. 1".
I haven't tried the TR6 lowering springs, but they should work on the TR4 as well. The exact height might vary a little from TR6, since there is some difference in weight (for example, the TR6 engine weighs more than the TR4's).
Later TR4 and TR4A went to a spring without a spacers, just like the TR6. And, this was a common swap in case of spring replacement by the service dept. So, the TR6 springs should fit without any problem. Just check that the rate is okay for your purposes, too.
Once the front is lowered, you'll need to work on the rear as well, or the balance of the car will be upset effecting handling and braking. The usual method is simply to make up some metal spacers (aluminum or ?) that go on top of the leaf spring, raising the rear axle height, which lowers the car. Here it's a straight shot, so a 1" thick spacer lowers the car 1". Longer u-bolts will be needed, too. And, I'd recommend any spacer have some provision for the pin on the top of the leaf that normally fits into a hole in the axle pad, to keep the two properly located.
Finally, once lowered you might find some bump steer or other squirreliness in the steering and handling. A quick check is if the tie-rods are close to level with the gound when the car is at rest. Might need to invert them, bend them or replace with another type, to get reduce bump steer, but this can vary from car to car depending upon with rack & pinion unit and the exact mounting of the R&P. Any anti-sway bar that's fitted will probably need some work, too, perhaps shorter end links or other adjustment.
Cheers!