The debates about "what is science", which raged thru the 20th century, are mostly historical now. And they were not definitively resolved. Like you, I am a latecomer to this historical debate, and cannot give you a definitive description of the current opinion on Lakatos. I will instead attempt to describe what conclusions I have drawn in my research on these questions.
The first candidate definition, that science is verificationism, hearkened back to Hume, and was championed by the Logical Positivists. LP was highly thought of for a time, but it is now nearly universally rejected as both an approach to philosophy as a whole, as well as its verificationist description of science. The primary problem with verificationism, is that we humans are built with strong confirmation biases, and almost any reasonably plausible idea can find cherry picked "verifications" for it. If we use verificationism for science, then looking for verifications will lead to all sorts of contradicting beliefs all of which lay claim to being "verified".
Popper's "Fasifiability" criteria was a significant improvement over verificationism, as it forces science to look at the hardest cases, and edge cases, which can refute a claim, rather than the "easy" ones which are invalidly used to claim "verification". Falsification is now widely applied across science, and Popper's criteria is widely accepted by practicing scientists.
Popper is not the final word, of course, because philosophers also like to do falsifiability tests of global claims, and falsifiability itself fails in many edge cases. Critics pointed out that science often ignores refuting test cases for highly useful theories for decades, that the overturning of theories by these refutations follows a more sociological process than Popper's rigid one, and that the methodologies cited by Popper do not apply to all sciences, as some sciences do not follow any common methodology with all other sciences.
The competing views offered included Kuhn's "normal science" vs kind of random "paradigm shifts", Quine and Wittgenstein offered a conception of science as just one of many possible coherent community practices, and Feyerabend challenged that science has ANY methodology or common criteria of validity, offering instead an "anything goes" characterization. While Popper's falsifiability clearly has exceptions, there were issues that most scientists and other philosophers of science had as well with each of these alternatives.
Lakatos' Research Programme proposal encompasses the strengths of each of these alternatives. It preserves the importance of refutations, and the search for them. It allows for long periods where a refutation is tolerated to a theory, so long as the Research Programme is working to close the apparent refutation. It provides a better explanation for when a paradigm shift occurs, and why, than Kuhn does. It allows that the methodolgies of different programmes may be slightly different, so long as they are seeking better explanatory power, and to close out challenging observations. Lakatos appears, to my mind, to have captured the strengths of each of these competing views.
A flaw for Lakatos is that his criteria for progressivity and regressivity was not calculable. The problem he encountered while trying to axiomize progressivity and regressivity was a reprise of the problem that Popper encountered while trying to axiomize Versimilitude. The process of empiricism involves JUDGEMENT, and cannot be spelled out in a closed form logical case. Lakatos had not realized this, similarly to Popper and his expectation that Verisimilitude could be calculable. My takeaway -- empiricists need to abandon formal logical truth as a truth criteria, and accept instead pragmatic truth as their truth criteria.
The one subsequent effort to characterize science I have encountered is E.O. Wilson's effort to define the scientific process as one where one compiles evidences incrementally and cumulatively, a process he calls Consilience. One way to look at consilience is as a useful clarification of what a progressive Research Programme looks like.
Note that each of these competing views of science is useful and valid for at least some of what science does. All of them involve useful insights, which their proponents then try out universalizing. My personal view on this is that Popper's falsifiability criteria is a highly useful first approximation to science, and that Lakatos' Research Programmes are the most useful and comprehensive of the clarifications/alternatives to falsifiability.
The relatively high regard that Popper is held in by most scientists relative to his rivals strongly supports my approach of treating Popper as a good first approximation, and Lakatos's Research Programmes as the higher order theory one sometimes needs to resort to when simple falsifiability is not precise enough.
But if this narration is not comprehensive enough, and if you want to find recent explicit philosophic commentary on Lakatos, and some alternative narrative to the one I have developed for myself by sampling the materials I have found on this old debate, you will need to conduct a current philosophic database search.