It is very confusingly worded, and I would think it's incorrect according to linguistic terminology.
A lemma is the canonical form of a word, commonly the infinitive of a verb, the nominative singular of a noun, and the positive of an adjective. The inflected forms belonging to a word would the the forms used for other tenses and persons etc for verbs, case and number for nouns, and comparative/superlative for adjectives.
This raises the question of what a word is, and there is no satisfactory answer to this, even more than 100 years after the foundation of modern linguistics...
Anyway, the 'boldface form' (a term I have not come across in 30 years as a linguist), refers to dictionary headwords, which are lemmas. There are some lemmas that are 'shared' by words which have multiple meanings: the common example in linguistics is bank, which can be a financial institution, the side of a river, a term to describe the process of tilting the wings of an airplane in flight, or it can mean to deposit an amount of money in an account, etc. All these words you would find under bank in a dictionary, but usually under several different entries. So I guess this is what is meant by "multiple boldface forms". However, these are usually completely unrelated words which by accident share the same spelling; in some cases it could also have been the same word that then developed different meanings.
To summarise: the paragraph you quote is plain wrong/sloppy in its use of terminology, as a dictionary headword is a lemma in every dictionary I have seen, but these are not unique, as several different words might have lemmas which are spelled the same way (but they are still different lemmas — no single word would have multiple dictionary entries).
- bank (bank, banks), noun: a financial institution
- bank (bank, banks), noun: the side of a river
- bank (bank, banks, banked, banking), verb: tipping the wings of an airplane
- bank (bank, banks, banked, banking), verb: depositing money in an account
We have four lemmas (in bold), two of which have two inflected forms, and the other two have three each. These are also four different words, with a total of four different word forms (bank and banks are common forms of all words)
Often, to avoid confusion, you would refer to them as $bank_1$ for the financial institution, and $bank_2$ for the river bank, etc. to indicate that they are different words.
You can probably see that English has a number of lemmata (which is the proper plural of lemma, since it's of Greek origin) which is by a factor of 3-4 smaller than the number of word types, whereas in other languages this ratio will be a lot smaller, as they have more inflected variants. An English noun has just singular and plural forms, whereas a German noun would have singular and plural across each of four cases (though some of them would share the same word forms).