Venus/Leo is fame from acting, Venus is probably the first triplicity ruler (up to age 28), which would make the figure diurnal. This narrows the range of Asc signs from Cancer to Capricorn. Of the choices, I suggest that Leo is the most likely the Asc (I use whole sign houses by the way).
4th/Scorpio = the father and ruler Mars/Capricorn 6th is consistent with the following description of her father on wikipedia:
Her father, Michael, is a former Wall Street trader and businessman who inherited his father's pasta business and has been in trouble with the law on several occasions.
Mother as a former singer and dancer is consistent with Moon/Taurus/10th and Venus/Leo.
Lohan's own party lifestyle leading to alcohol/drug abuse leading to trouble with the law can be seen from Venus/Leo/1st ruled by Sun/Cancer/12th.
Opposition from Mars/Capricorn/6th worsens the problem and also makes her accident prone.
Moon's configuration: In Taurus/10th, Separates from square to Venus/Leo/1st and applies to Jupiter/Pisces 8th. Delineation: Her need for pleasure is satisfied by fame from singing, dancing, acting and partying (Venus/Leo) which leads to self destructive addictions to alcohol and drugs (Jupiter/Pisces/8th).
A quick way of finding the precise degree of Leo would be to check for transits of the nodes or Saturn to the angles at the time of important incidents for which a public record exists.