Lyman’s Law is a rule that governs the voicing in jukugo (熟語)  – words in Japanese that consist of 2 or more Kanji (Kanji is the word for Chinese Character taken in Japanese).

“There can be no more than one voiced obstruent within a morpheme.”

An obstruent is a consonant that is made by blocking air passing.
Here are the changes that take place under Lyman’s Law, similar to one of those taken under Grimm’s Law:

So, if in a second part of a compound Kanji, there are no syllables beginning with g, z, j, d or b, then the first syllable will usually morph into a voiced consonant. This is displayed with a dakuten (濁点): は、ぱ、ば, these are the circle or the two dots next to the は character. These are the symbols in hiragana (one of the Japanese syllabaries) that represent the voiced consonant.

An example of this is in the words for “firework” and “spark”, the word for fire is hi、ひ、火 and flower is hana、はな、花.  The three representations are romaji (Latin alphabet), hiragana, then the kanji.

• Firework: hanabi、はなび、花火 literally flower fire. Note the dots on the “hi” to show the hi becoming b as shown in the chart above. The kanji do not change, there is no reason to suspect that it wouldn’t be pronounce hanahi, but it changes to hanabi because of Lyman’s Law
• Spark: hibana、ひばな、火花 literally fire flower. The dots this time are on the “ha” turning it to “ba” because this is the second kanji in the word and there isn’t already a consonant with the dots forming a voiced obstruent.

If there is a “voiced obstruent”, aka a syllable beginning with a g, z, j, d or b, then no change happens to the two independent words such as in:

• hitori means alone (ひとり、一人), tabi means travel (たび、旅), together they form travelling alone: hitoritabi (ひとりたび、一人旅), not that “tabi” doesn’t change at all, this is because of the “bi”, it is already voiced so that ta does not become “da”.

That concludes the very short explanation of Lyman’s Law.

As with all rules, because language is natural, it isn’t without exceptions, this includes in Japanese names where the changes either happen or don’t happen for no reason.