.yes
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It would be much more accurate to say that the northern border of the State of New York runs "across" Lake Champlain.
Lake Champlain
Lake Champlain forms part of the border between Vermont and New York.
what lake forms the northerm borders of Ohio
lake Ontario and Lake Erie
Lake Superior
Lake Champlain.
Lake Champlain is a redefined border between New Hampshire, New York, and Vermont. It also forms a border between the US and Canada.
Lake Champlain
Lake Eire forms the NW border of Pennsylvania between Ohio and New York State.
Lake Erie and Lake Ontario and the Canadian Provinces of Ontario and Quebec.
Lake Champlain forms part of the border between Vermont and New York.
Lake Erie and Lake Ontario and the Canadian Provinces of Ontario and Quebec.
Where it is not following the center-line of Lake Erie and Lake Ontario and their connecting waterways, the latitude of the northern border of New York State is 45 degrees north.