there is a stirah in tosfos taamah tosfos said before hechsher mitzva is not like mitzva and here we say it is? the aruch lanair says there you can do on weekday here you can't bec. the liquid would become solid.
but can't you cook it on erev shabbos and keep it cooking on shabbos?
F. Lax
I think the simple answer is that practically speaking it is not possible to keep the lead of the wick boiling-hot over Shabbos for a sufficiently long period of time. Don't forget that capital punishments are carried out only in the daytime (see Mishnah Sanhedrin 32a) so this would mean that the lead would have to be kept hot overnight. Someone who learns the 3rd chapter of Maseches Shabbos sees that it was quite a hard job to keep food warm overnight on Shabbos (in fact nowadays we also don't always find it so simple to do this without the food getting spoiled or burnt up, etc.) and to keep the lead hot enough without it all evaporating overnight would be very hard.
(See Tosfos Pesachim, end of 75a, who does in fact write that one could boil up the lead on Erev Shabbos, as you suggest. However it seems that our Tosfos maintains that while this may be theoretically possible, in practice it cannot be done).
KOL TUV
Dovid Bloom
Here is an additional aspect about keeping the lead hot enough until the penalty is carried out. The best way of keeping the lead hot, when possible, is to use "Chamei Teveryah" - the hot springs of Tiberias. (This also avoids the problem of "Shema Yechateh" -- one may not use a wood or coal fire on Shabbos lest one stoke it to make it burn better.) The Chamei Teveryah are extremely hot and might be able to melt lead; see the Gemara in Shabbos end of 39a which mentions that they pass by the gates of Geihinom.
This might resolve the discrepancy between the Tosfos in Pesachim that I mentioned previously, and the Tosfos in Yevamos. The Tosfos in Pesachim refers to a case where Chamei Teveryah are available while our Tosfos refers to a scenario where they are not available.
KOL TUV
D. Bloom