A sidewinder has the coils laying on their sides, so they point sideways - towards the bridge and neck, instead of both pointing up towards the strings.
Most sidewinders have very typical coil dimensions. The coil is fairly "square" in that it's more or less as tall as it is wide, or within a 2:1 factor or so. But some cigar box sidewinders have very narrow, very tall coils - such that when they're laid sideways, they form a very thin, but very wide pickup:
View attachment 4351934
But again, I don't think that's what the Lace pickup is. Lace does the whole alumitone thing as their signature style. An alumitone pickup is essentially a very low impedance pickup that uses a transformer to boost the voltage of the signal and match impedance to what the controls and amp can handle.
Consider that a normal bass pickup might have 5,000 - 10,000 turns of wire on each coil, and the wire is very fine (usually around 42 gauge) and fairly high resistance - so, the pickup's DC resistance is somewhere in the 5 - 15k ohm range, and the signal produced is usually in the couple-hundred millivolt range, or even above a volt or two. This combination of voltage and impedance is what amps are designed to work with so you can wire the pickup and passive controls directly to the jack.
By contrast, a low impedance pickup often has one "turn" of "wire," or sometimes just a few turns. And often the wire isn't even actual wire. The "wire" is much, much heavier gauge and the resistance is close enough to zero that it might as well be zero. The lace pickups literally use the aluminum frame as the coil wire - it's just an aluminum plate with a hole in it. The voltage in the signal produced by this style of pickup is several orders of magnitude lower than a conventional pickup, so a transformer coil is used, offline from the sensing "coil" to boost the voltage and get the impedance up from near-zero to the several-k ohm range that'll work with an amp.
The main difference in terms of the signal is that a low impedance pickup doesn't have any coloring from the resistance of the coil wire. The sensing is done in a circuit that is closer to "perfect" than a conventional coil, and then that "perfect" signal is boosted afterwards. Typical passive pickups get some treble roll off and then a hump of a resonant peak in the high mids, as a result of the loading on the coil. A low impedance coil boosted by a transformer doesn't end up with that same filtering. It is, in a sense, a similar concept as using a conventional pickup with an active preamp. The thing is, an actual "perfect" signal with no tonal coloring at all is not what people are used to, so to a lot of people, it sounds unusual and undesirable. Most pickups of this design have elements in the design that are basically a bandaid at adding some color back in to keep the signal from sounding too sterile, so it's kind of hard to see the "it's a perfect signal" thing as an advantage.
Anyways, I hope that helps in terms of understanding, without having to rip one apart. But on the other hand, if you do rip one apart I hope you show us all what you find.
Of course, you can always EQ out the stuff you don't want, but it's harder than it sounds IME to try to recreate the mid or upper mid hump/bump that some famous designs have. Lo-fi with strong mid bump to me sounds like it would call for a humbucker with magnets on the weaker side and lots of wire to compensate for the lower output. Lots of ways to skin the cat though. 
