I will be conducting the seder in the house of a non-religious Jew (both nights). The problem is that they will be turning on the lights during Shabbos, and certainly during Yom Tov. (For example, on Saturday afternoon/evening they will turn on the lights. They are not going to keep the lights on for two nights).
Without these lights, there would be some illumination from the street, but not enough to be able to read the Haggadah or to eat. What should I do (I cannot benefit from chillul Shabbos/ yom tov, and I must read the Haggadah)? Is there anything I can rely on to benefit from these lights, if I cannot convince the person to leave them on, or I cannot trust them to do so (they might say that they will leave the lights on, but in fact they will perhaps mess with them during Shabbos/ yom tov)?
Assuming these are people who were raised non religious, there is room to give them the status of Tinokos Shenishbu, meaning they are not considered to be purposefully breaking Shabbos. This melacha is being done for themselves and not for you. One may benefit from unintentional Shabbos violation done by another, in a case of need. The melacha done by such a person is questionable if we treat it as intentional or unintentional. In addition if it is a fluorescent light there are opinions that this involves only a Rabbinic prohibition which adds another element of leniency.
If you request of them and they say they will leave it on, being that this does not involve great financial loss, there is reason to believe they would respect your request. The first night presumably the light will have been on from the daytime. Since it is a case of need to run the seder for these people, it would seem based on the above that you could be lenient to run the seder in their home.
See Shulchan Aruch O:C 318:1 and Mishna Berura, Biur Halacha and commentaries there.
See Chu”t Shani Vol. 2 pg. 47 who remains in doubt as to the status of melacha done by the typical irreligious Jew.