I'm simply a guy that has taken care of our 22 acre ski lake off and on over the last 20 years (not a professional). Obviously, you can avoid chemicals altogether, but the plan-of-attack is limited. That would largely entail dyes and sterile grass carp. The downside of dye is it is dilutive (in the event of heavy rains---flushing water out of the outlet). Grass carp take about 3 years before they reach their full consumptive potential. Their consumptive potential plateau for a couple years, and then decline. After year 7 or 8 they are simply 5 foot long monsters just swimming around with substantially reduced consumptive strength. Candidly, I like grass carp as a control method, but you will need to re-supply about 20% annually in order to keep the collective stock consuming in the optimal "plateau" range.
As to "chemicals", if you want "easy" look into Sonar or Tradewinds. Both are easy/quick to apply. Downside is that you may not be able to irrigate lawns from the lake for 90 days, and you'll need to be careful about other restrictions. Tradewinds is used by many to primarily control Duckweed, but I have found it effective (at times) with general evasive weed growth---except for large and small pondweed. A product by the name of Aquastrike may also be a good bet. As I understand it, Aquastrike is essentially a "cocktail" of Clipper and Diquat (i.e. my novice take). A key advantage over Sonar and Tradewinds is the fact that Aquastrike is a contact herbicide, with limited irrigation restriction. A disadvantage is that you have to dilute the product with a lot of water, which makes it much more time-consuming and equipment intensive to apply (with 3 or more applications needed during the skiing season). As to Aquastrike, if you can get it on without a heavy rain within a few days (i.e. flushing water out of your lake), it should do a good job. Sonar and Tradewinds, conversely, work over a period of weeks (not days) and quantities applied will dilute in the event of a "flushing" rain. All-in-all, I have found that chemical weed treatment is an "art", not a "science", and timing, weather conditions, chemistry, and follow-up are all very important. Also, the chemical that worked good last year, doesn't always work well the next year. Like BCM stated above, this is why many hire local, licensed professionals.