Long wood screws into the vertical STUDS behind the horizontal lath strips are pretty solid. BUT they can be hard to find! On a sheetrock wall, you use a magnet detection device to detect the heads of the screws holding the sheetrock to the studs, but that works because those heads are just barely below the front surface. With plaster over lath, the thickness of the plaster can be easily ½" to even a full inch thick, so you'll never detect the nails in the lath strips. Good starting point, though: most electrical mounting boxes in the wall were fastened to the side of a vertical stud. So on one side or another of any such box, try drilling a small hole with a long bit. If you drill through nothing but plaster, you'll feel one change from drilling plaster to nothing. If you drill though plaster and then through a lath strip, you'll feel plaster, then a change to something a little tougher (lath strips are only about ¼" thick wood), then nothing. If you drill into a stud behind all that, you'll feel you are drilling though solid wood (after the plaster) as far as you can go - the stud is 4" thick behind the lath. You may have to drill a horizontal line of several holes to find the stud, so you'll have patching to do. BUT one you find one stud, just measure horizontally in 16" steps in either direction, and try the drill probe again to confirm there is a stud there, too. NOTE that door frame and window frames do NOT always follow the 16" custom - those items are placed where they need to be.
If you want to use hollow-wall anchors, there are many. The simpler ones like this
Everbilt Plastic 14-16 x 1-1/2 Screw Anchor with Screw Green,124999: Amazon.com: Industrial & Scientific
www.amazon.com
come in various sizes depending on the screw diameter you plan, and require you drill the correct hole size (specified on the package) in the plaster. These will hold lighter objects and framed pics. I recommend this type for most light items. A plain nail into the plaster wall generally will not hold tightly, although a long nail tapped in at a 45 degree angle will hold better. But these tapered poly sleeves with ridges on them expand when you screw in the screw, and that holds them solidly in the correct-diameter hole.
Toggle Bolts like this
Amazon.com: 1/8X2 Combination Mushroom Head Toggle Bolt Zinc (Pack Qty 50) BC-0632TBCM by Korpek : Industrial & Scientific
www.amazon.com
will hold a heavier load because those two arms spring out behind the wall, and then you tighten the screw to pull the arms against the inside of the wall. Hopefully they grab onto SOME of the lath strips. Most come with a very long bolt so they can be used with a wide range of wall thicknesses. These require that you drill a much larger hole to get the folded arms onto the wall. Be aware if you unscrew the long bolt, the inside piece falls off and you have to start with a new toggle bolt. But that makes them easy to abandon - just patch the hole.
These Toggler anchors
TOGGLER Toggle TB Residential Drywall Anchor, Polypropylene, Made in US, 3/8" to 1/2" Grip Range, For #6 to #14 Fastener Sizes (Pack of 100): Hollow Wall Anchors: Amazon.com: Industrial & Scientific
www.amazon.com
are all polypropylene. Their arms fold in to a small diameter to be pushed into the holes in the wall, but then spring out to the side once the unit is through the wall far enough. Then you screw in the screw. NOTE, though, that these work best when the wall thickness is close to the spacing between the front flange and the spread-out wings.
Molly Bolts
ISPINNER Heavy Duty Wall Anchor Gun Metal Setting Tool with 18pcs Molly Bolt Hollow Drive Wall Anchor Screws Assortment Kit for Cavity Anchor Plasterboard Fixing: Amazon.com: Industrial & Scientific
www.amazon.com
can hold up more weight than most because they spread out behind the wall a set of four arms to spread the load. That set comes with a selection of sizes and a tool. You drill a hole the right size and inert the bolt, then back out the screw a bit. Use the tool to pull the screw head out, causing the "wings" inside the wall to spread out. Note that, on the front side of the wall, the bolt has a small flange. So one it's installed, you can actually remove the screw, and the rest of the bolt stays in place. Then you can re-install the screw and tighten it up to hold you load. ALSO note that, if you are trying to abandon this device, it still shows you that front flange and hole, and you can NOT pull it out of the wall OR push it all the way in. So covering it up is a bit more work. Molloy Bolts come in various diameters for different loads, and also in various lengths. Pay special attention to the specification of the wall THICKNESS each is designed for - that's the thickness from the back of the front flange to where the innner four "arms" will bend outwards inside the wall. I never has that special tool. I just bought the right bolt size and tightened the screw to make the inner wings spread out until the screw became tight, then I unscrewed it, mounted the bracket (or whatever) on the screw, and re-installed it.