Depending on the storyteller, "LA" means either "late A" or "light A" and indicates any of the late, narrow wedge-head versions of Chrysler's A engine: 273, 318, 340, and 360. The original A engine had polyspheric combustion chambers had several different displacements, although the 318 is the most common. A engines used two centrally-located valve cover bolts but the LA used 5 around the perimeter of the valve cover flange. The LA was a redesign for 1964 to fit a small-block V8 into A-bodies (273 only until 1968).
The chart shown above is incorrect. There is no "casting number" for T/A heads; the difference is in the machining. All 1970 340s were supposed to have 915 heads. I've yet to encounter an untouched, original '70 engine with 894 (a.k.a. "X") heads but I'm sure they exist. The 915 heads are colloquially called "J" heads, as many have a large, >1" letter "J" cast near the spark plugs. Other letters that might be cast in that area are O,U, and Z. The letter will not tell you if they are T/A heads either. You must look at the location of the intake pushrod holes. All J heads use the same casting; the T/A heads require special intake rocker arms not used on any other cylinder head.
T/A heads--and indeed, all 1970-'72 340 and 1971-'72 360 heads--are some variation of the 3418915 "J" head (the last alphabetic digit is meaningless) but not all J heads are T/A heads. The vast majority of them are not. 360s and late 1972 340s used 1.88" intake valves; 1970-very early '72 340s used 2.02" intake valves. All J heads used 1.60" exhaust valves. Any 1.88" head can be a 2.02" head simply by grinding the intake seats for the larger valves; there is no inherent extra value in an original 2.02" head. Conversely, one cannot (easily) turn a standard J head into a T/A head since the intake pushrod holes are located differently. The original pushrod hole would need to be filled somehow before redrilling in the T/A location... and then you'd need to locate the rare, dreadfully-expensive T/A rocker arms.
There is no way at this point in time to even tell which engine, never mind which car, on which the heads were originally installed unless A) you pulled them yourself off a known original car or B) they're T/A heads, in which case they came from a Challenger T/A or AAR 'Cuda (340 with three two barrels). As mentioned, any small-valve version becomes a large-valve version with a simple, inexpensive valve job.
In terms of performance, they're a bit better than the '68-'69 894 X head by virtue of a slightly-better exhaust port. The T/A heads perform no better than other J heads; the pushrod was moved to allow greater porting but the port itself was not changed--it was a DIY deal. The only better factory head is the late-'80s/early-'90s truck "308" casting, to my knowledge. The J heads were replaced by the inferior "587" casting on 340s and 360s for 1973.
Take a picture of the whole head from the valve cover side, and one of us can tell you whether you have true T/A heads or just basic 340/360 heads.