Can Dragonfly make it to one of Titan's Lakes?
tl;dr: Yes! It could be doable in 2-3 years.
According to your linked document Dragonfly will use a Multi-mission radioisotope thermoelectric generator or MMRTG:
The MMRTG design incorporates PbTe/TAGS thermoelectric couples (from Teledyne Energy Systems), where the TAGS material is a material incorporating Tellurium (Te), Silver (Ag), Germanium (Ge) and Antimony (Sb). The MMRTG is designed to produce 125 W electrical power at the start of mission, falling to about 100 W after 14 years. With a mass of 45 kg the MMRTG provides about 2.8 W/kg of electrical power at beginning of life.
The MMRTG design is capable of operating both in the vacuum of space and in planetary atmospheres, such as on the surface of Mars. Design goals for the MMRTG included ensuring a high degree of safety, optimizing power levels over a minimum lifetime of 14 years, and minimizing weight.
See also MMRTG fact sheet.
The MMRTG uses plutonium-238 with a half-life of 87.7 years which is a mean life (1/e) of 126.5 years. That means that after 14 years the radioactive and therefore thermal activity of the plutonium itself will drop to 89.5% of it's original value.
The quoted 14-year drop (125 W to 100 W) is 80%, so it looks like there may be other sources of degradation being taken into account besides the radioisotope itself. The semiconductor material used to make the thermoelectric conversion is one possibility.
While the decay of the radioisotope is exponential (which means it never goes to zero) other sources of degradation may drop linearly or even accelerate, so we can't extrapolate in a simple way beyond 14 years.
Your linked document says:
Flight performance analysis14 suggested that the maximum-range speed (Fig. 4) would be about 10 m/s, and that flight power for a representative 420-kg vehicle at this speed would be a little over 2 kW. A 30-kg battery at 100 Wh/kg could theoretically permit
flight for 2 h and achieve some 60 km in range. In practice, battery performance would be heavily margined for safety and performance would be lower.
Figure 4. Rotorcraft power curve for a representative vehicle mass of 420 kg on Titan. The induced power required for rotor thrust falls toward higher speed, whereas the body drag increases quadratically and eventually dominates. These competing factors define the maximum endurance speed (the minimum in the curve ~8 m/s) and the maximum-range speed (where the tangent to the curve passes through the origin, corresponding to ~10 m/s). Titan’s dense atmosphere and low gravity means that the flight power for a given mass is a factor of about 40 times lower than on Earth.
Figure 7. Energy management and communication concept of operations. MMRTG continuously recharges the battery, but downlink and especially flight demand significant energy. Activities can be paced to match MMRTG in situ capability while maintaining healthy margins on the battery state of charge.
Figure 7. also suggests roughly 2 hours of flying per "day" which is about 16 Earth days, followed by a slow recharge.
Except during polar summer or winter, operations of a lander on Titan with DTE communication are paced by the Titan diurnal cycle. A Titan solar day (Tsol) is 384 h long (16 Earth days). Seen from Titan, Earth in the sky is always within 6° of the Sun. Interaction with Earth, and logically any operations requiring real-time observation (such as atmospheric flight), occur during the day, and nighttime activities are generally minimal and power can be devoted to recharging the battery. Thus, a logical maximum size of the battery is that which completely captures MMRTG power during the Titan night, or 75*192 = 14 kWh. Such a battery—about a quarter of the size of the battery in a Tesla electric car—would be rather massive (140 kg), assuming a representative specific energy metric for space-qualified batteries of 100 Wh/kg. In practice, a smaller battery may be chosen, sacrificing some energy-harvesting efficiency for lower mass and cost.
So at 60 km every 16 days (3.75 km/day), you can travel 1370 km per year. That takes you from the equator to +/- 60 degrees in 2 years, and to a pole in 3 years, using 50 to 100 charge/discharge cycles of the lithium ion or LiPo batteries depending on how you do it.
This is a much shorter time than the MMRTG's shelf life, so that should not be a consideration.
There are of course a variety of dangers to face and things that can go wrong along the way (see for example How quickly might a Titan rover or drone get covered in oil and dirt? Will it need windshield-wipers?), and that would make an excellent next question!
