Given a Latin noun, how does one transform it into an adjective meaning "lacking [noun]" (the equivalent of English "-less")? I know that "having (a lot of) [noun]" would be formed with the ending "-ōsus"; what is its opposite?
Latin seems to be far less uniform in this than English. Unfortunately there is no single way to derive adjectives indicating a lack. Here are some possible ways:
Someone without cura is securus, but the prefix se- is quite rare in this use.
As Cerberus mentions, in- is more common, as in infamis has no fama.
Someone without forma is deformis, and de- seems to be more productive than se- and I get the impression that it is more common than in-.
In particular, if you want a word for someone who used to have something but no longer has, the combination of de- and -atus is a good option. For example, decoloratus would be "discolored" (as opposed to coloratus, "colored") and most would understand that debarbatus has had their beard shaven off.
There are several possible prefixes, and they are sometimes combined with suffixes. In some cases several prefixes reach the same goal: demens and amens are roughly the same. There seems to be no semens or immens, and the latter would be easily confused with immensus.
It probably depends on the noun, but the normal negative/privative affix is in-, which is related to English un-, Greek a(n)- (the alpha privans), and all/most Indo-European negations with nasal sounds (Latin non, English no etc.). Then you add any of the semantically week adjectival suffixes such as -us, -osus, -is, -lis, etc. Examples:
dolor - indolorosus/indoloris "painless"
cura - incuriosus "careless"
anima - inanimalis/inanimus/inanimis "breathless, soulless"
Note that it is not always easy to establish whether a word is derived from a substantive, adjective or verbal stem, since all are often similar or the same.