I like to structure my understanding and strategy of lucid dreaming around the timing of REM cycles. I'll say there are six, but in practice there is usually five with the sixth being any time beyond normal fifth. The science behind sleep cycles is covered elsewhere in depth, so I'll just summarize the basics so I can get on to some personal and practical experience on each cycle.

Sleep Cycle Basics
Briefly, each cycle takes you through all the phases of sleep in about 90 minutes (which can vary per person and per night). Don't confuse phases and cycles. The phases (or stages) are REM and the varieties of NREM (usually categorized on a scale from light to deep). A cycle goes through all the phases with a mix of NREM and REM, and then repeats. The portion of time spent in REM increases progressively in the later cycles. At the end of each cycle, there's a chance of a brief waking. With intent and practice, one can extend those wakings long enough to recall and record dreams from the cycle that just ended.

I'm focusing on REM here. While it may be true that you can have dreams or conscious activity in NREM, it's really not conducive to mainstream LD practice. If you're into neuroscience or really advanced clear light dream yoga stuff, then explore NREM. But for lucid dreams, REM is where it's at.

If you sleep 7-8 hours, you have five sleep cycles per night. Even if you sleep more or less than that, it's probably the case that your cycles are longer or shorter, not that you have more or fewer cycles. If you wake with an alarm, you're probably interrupting cycle 5. If you have a very demanding schedule with little sleep, you might be interrupting cycle 4 which probably results in a constant sleep debt. On the other hand, if you really want it and have the extra time, you can go beyond cycle 5 into cycle 6. The best way to identify the cycles is to wake up after each one naturally and note the time.

The 6 Sleep Cycles
Below are my observations on each cycle, along with some of the common sense and knowledge stuff you've heard before. The times assume 90 minutes for each. In practice, times tend to be a bit longer because it takes time to initially fall asleep and there's time between the cycles. So for example, cycle 4 probably starts closer to 5h and cycle 5 might run closer to 7h-8.5h depending on lifestyle.

Cycle 1 (0h-1.5h)
REM is shortest in this cycle, maybe as little as a minute. I rarely recall any dream activity in this cycle. If I wake after cycle 1, it is not very pleasant. I only recall a burst of emotion with no apparent cause, often negative like anger or anxiety. And I will feel unrested the next day. If I wake after a cycle 1 dream, it means my intent is very good, perhaps too good. I'd rather not push so far into this cycle because I'm likely interfering with NREM and sabotaging my sleep quality. When I wake after cycle 1, I take it as a sign to take a break for a few days to let my intent revert back to a more balanced level.

Cycle 2 (1.5h-3h)
Dreams tend to be short and strange. I can recall dreams, but I don't bother trying LD here. If I recall a dream after cycle 2, then I know my intent is at the optimal level and I am set up for a good night in the later cycles. Assuming I recall one dream each for cycles 2-5, that's four dreams in one night and that's my target. It is possible to record more than four, but it would be because cycle 4 or 5 was divided into two or more shorter segments, or because I chose to sleep longer for cycle 6. It takes practice to reach recall at level, but getting an extra waking between 2 and 3 for an extra session of MILD can boost results later in the night.

Cycle 3 (3h-4.5h)
Dreams are shortish. LD is possible, but I only attempt DILD, not WILD. DILD is usually started by recognizing a dreamsign and a reality check, not spontaneous. So, only when I am very diligent with my waking practices do I have a chance to LD in this cycle. But if I become lucid, these dreams are very emotionally charged and memorable even if they are short. DEILD-chain seems too difficult here. For non-LD, I tend to measure my recall by how much detail I record for the cycle 3 dream. While cycle 2 is the goal for the first recall, it's cycle 3 when dreams become more understandable so they are a better test of quality vs quantity. It's a great benefit to have good recall after cycle 3 because then you are awake to insert a WBTB between 3 and 4. If you don't wake naturally after cycle 3, then you have to use an alarm which I don't like.

Cycle 4 (4.5h-6h)
This cycle is the sweet spot. LDs are more frequent and longer than cycle 3, and more stable and vivid than cycle 5. Before this cycle is the first oppurtunity for WBTB and/or WILD. Dreams are just the right length and weirdness to be good for DILD, so leading into cycle 4 with MILD/SSILD is an optimal strategy. DILD's start with a mix of dreamsign vs spontaneous. This is also the cycle that is most affected by REM rebound, supplements, or anything else that alters REM quality and duration. Although I have fewer cycle 4 LDs than cycle 5, cycle 4 is the one I target for the best lucid dreams. I can usually get one good DEILD-chain if the LD ends early. Some chance of multiple dream segments, but not as much as cycle 5. For non-LD, I should have good recall of cycle 4 dreams. If not, then something is off and I'm probably not prepared for success in cycle 5 either.

Cycle 5 (6h-7.5h)
This is the last cycle in a typical night, so it should be the one with the most REM. But maybe not. If you use an alarm to wake in the morning, this is the cycle you are interrupting so you're losing REM time and maybe recall too. Before this cycle is the second oppurtunity for WBTB/WILD, but there's a greater risk of not being able to fall back to sleep. Dreams might be more realistic, ordinary, boring. DILDs tend to be more of the spontaneous variety. More LDs come in this cycle but with a wide range of quality. Often they are very short or lack control. Since they are the most common, it's the best time to experiment with techniques of stabilization and control. False awakenings are more common. DEILD-chaining is easier and can happen multiple times. A good cycle 5 LD can be really really long; so long that you start experiencing apparent time dilation. Because sleep is lighter here, cycle 5 might be divided into two or more segments that are treated as separate dreams. If there is a waking in the middle of the cycle, it's another decent oppurtunity for WILD. REM atonia is not quite as pronounced, so it's more likely to wake from an a LD because trying to move my dream body results in moving my waking body. If I don't use an alarm, I should always recall something for cycle 5 as it's the final waking going into the morning.

Cycle 6 (7.5h+)
I think people usually don't sleep into a 6th cycle. If you sleep more than 8 hours, it's probably because your cycles are longer than 90 minutes and because there's extra non-sleep time at the beginning of the night and between cycles. To get to cycle 6, you need to make the conscious effort to sleep longer than feels natural, or because of sleep deprivation beyond typical REM rebound. Cycle 6 and beyond are almost all REM. Sleep is very light and tends to drift in and out near the edge of waking. This makes it ripe for WILD/DEILD type induction though LDs may be very short and unstable. False awakenings are frequent and I might get stuck in a false awakening loop. It's good practice though, if you can arrange a day when you can sleep that long.