I'm a little puzzled by the lens being called a 'Portrait Anastigmat'. The name is almost a contradiction in terms
The Dallmeyer Portrait lens was of the Petzval type, Ian has already posted you a link to information on this.
The Pertzval lens has four pieces of glass, the front two being compound (stuck together )
"Anastigmat" was first coined by Carl Zeiss in 1889. I simply don't know when the word would have appeared on a Dallmeyer lens, but obviously later than this. An anastigmat lens is more highly corrected than the Petzval and so may contain more glass, but without finding more info on the lens I'm not sure of the configuration, so can't advise exactly how to dismantle it. A quick google didn't help. I've several Dallmeyer lenses in my collection, but alas not this one. I might be able to find something in my books, I'll report back if I do.
Some general advice, though... the lens is probably 100 years old or so. Leaving it as it is for a little longer will not do any harm. Incorrect cleaning or cross threading the elements when re-assembling could scrap it completely.
Cleaning isn't difficult, but I've seen some terrible adviced given out on the interwebby thingy. DO NOT be tempted to rub the lens gently with a blob of toothpaste on your finger!!! :o Do not use acetone, either, it seperates the cemented surfaces. The safest solvent to use is probably either pure propanol or ethanol. There are better solvents to use but they are difficult to obtain, these days. Thanks to all the health and saftety rules modern 'Lens cleaning solution' is usually mostly water with a bit detergent and maybe a spot of propanol it. It doesn't do any harm to the lens but isn't that good a cleaning it either The idea is to try and wash the lens, rather than scrub it with a dry lens cloth. If it is very mucky then you will end up with a scratched lens. A good technique is to blow off as much dust as you can first, use wooden cotton budes dipped in the solvent of your choice and gently work around in a spiral from the centre to the outside. Keep changing the bud and expect to take a good few minutes going over each surface several times. Be careful not to get compound lenses too wet, there is a risk of capillary action pulling the solution into the edges of the lens mount and ultimately even between the elements. Lens surfaces that were inside the barrel really shouldn't be that dirty and a gentle clean with a little solvent on a cotton bud or with lens tissue is all that should be needed. The only surfaces that should ever be at risk of getting get really filthy are the front and rear - in extreme cases unscrew the element, put a drop of detergent (photo flo is fragrance and colour free detergent) on the glass and wash it under warm water from the tap using a bud or lens tissue to get the stubborn bits off. This will do much less damage than scrubbing with a dry or damp lens cloth or tissue, but obviously use your common sense about getting water into places it shouldn't go. If after careful cleaning it is still hazy then you may have either cloudy balsalm or mould growth. Either of these is pretty bad news and may mean either professional help or a 'show piece only' lens.
Can you get a macro picture of the lens elements? Mould has a definate look to it, it might be recognisable from a picture.