Mostly no they can't, various and random surveys/tests found in many cases hearing did better. The question doesn't really address the hostility some deaf feel about linking lip-reading to speech so anti-sign, anti-culture at the base of it. The primary issue (In the UK anyway), is the classes are not appropriate, or structured, and approaches do not actually include deaf people!
To master any sort of lip-reading, you have to start very early on, and most who attend classes go there as a last resort not a first option, get discouraged, and do not go back, some only lasting a few weeks at most and then giving up. The reality that effective progress relies ON having useful hearing rather defeats the point of teaching those already deaf. As does the pupil make up deters young people.
The UK system is 6 monthly at most in nature, aimed at those with residual hearing and with a duration of about 2hrs a week, hardly any tuition that includes on the street practice where it is needed. It's viewed as 'oralism/audism' by some deaf who oppose it being used in schools.
Classes also polarise by in most cases, so that fellow students struggling with hearing will struggle with those with hearing aids who in reality are probably LISTENING more than they are lip-reading. It is debatable a sole teacher can teach one person effective lip-reading let alone a class of 12 or more. The same token is mooted via BSL being taught via captioning means, nobody looks at the sign much. It is why BSL users often produce signed output with no captions which they claim is real awareness but in reality, just means those who don't understand sign will just switch off.
There is little doubt text in its various forms and accessible formats has demoted BSL to a major extent as necessary. Media is text driven deaf-wise, not sign-driven. Lip-reading you could not hone as any skill via media again because subtitling removes the effort needed to try and 99% of media output is not geared to lip-reading. On the street, the 'Face me and speak clearly..' advice is pointless and unviable. Access to lip-speakers for support is almost impossible. Unless a major change of approach is made with regards to teaching those losing hearing more viable access formats, lip-reading is not going to work.
Demands for an inclusive 'communication' class approach would be the sole way to enhance access for most, and one on one intensive, but the polarised approaches to communication, the HoH reluctance to adopt sign, and the Deaf reluctance to adopt lip-reading etc, defeat any attempt to try it.